CIE 15: Technical Report: Colorimetry, 3rd edition

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Document Name: CIE 15: Technical Report: Colorimetry, 3rd edition

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Standards Body: international Commission on Illumination

ISBN 3 901 906 33 9

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Y

CIE 15:2004
3rd Edition

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535.66
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612.843.31
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Descri ptor : Coiori metry

Colour of objects
Colour vision
Perception of colour

CIE 15:2004

This Technical Report has been prepared by CiE Technical Committee 1-48 of Division 1
"Vision and Colour" and has been approved by the Board of Administration of the
Commission Internationale de I'Eclairage for study and application. The document reports on
current knowledge and experience within the specific field of light and lighting described, and
is intended to be used by the CIE membership and other interested parties. It should be
noted, however, that the status of this document is advisory and not mandatory. The latest
CIE proceedings or CIE NEWS should be consulted regarding possible subsequent
amendments.

Ce rapport technique a ete elabore par le Comite Technique CIE 1-48 de la Division 1 "Vision
et Couleur" et a ete approuve par le Bureau de la Commission Internationale de I'Eclairage,
pour etude et emploi. Le document expose les connaissances et I'experience actuelles dans
ie domaine particulier de la lumiere et de I'eclairage decrit ici. II est destine a etre utilise par
les membres de la CIE et par tout les interesses. II faut cependant noter que ce document est
indicatif et non obiigatoire. II faut consulter les plus recents comptes rendus de la CIE, ou le
CIE NEWS, en ce qui concerne des amendements nouveaux eventuels.

Dieser Technische Bericht ist vom CIE Technischen Komitee 1-48 der Division 1 "Sehen und
Farbe" ausgearbeitet und vom Vorstand der Commission Internationale de I'Eclairage gebilligt
worden. Das Dokument berichtet uber den derzeitigen Stand des Wissens und Erfahrung in
dem behandelten Gebiet von Licht und Beleuchtung; es ist zur Verwendung durch CIE-
Mitglieder und durch andere Interessierte bestimmt. Es sollte jedoch beachtet werden, daB
das Dokument eine Empfehlung und keine Vorschrift ist. Die neuesten CIE-Tagungsberichte
Oder das CIE NEWS sollten im Hinblick auf mogliche spatere Anderungen zu Rate gezogen
werden.

Any mention of organisations or products does not imply endorsement by the CIE. Whilst
every care has been taken in the compilation of any lists, up to the time of going to press,
these may not be comprehensive.

Toute mention d'organisme ou de produit n'implique pas une preference de la CIE. Maigre le
soin apporte a la compilation de tous les documents jusqu'a la mise sous presse, ce travail
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© CIE 2004 - All rights reserved

CIE 15:2004

This report has been prepared by the Technical Committee 1-48 "Revision of CIE document
15.2 Colorimetry" of CIE Division 1 "Colour and Vision" by using previously published material
of the CIE and considering resolutions of the CIE Division 1 meeting at Teddington 2000-04-
06 and Rochester 2001-06-22/23. This present publication replaces CIE 15.2-1986
"Colorimetry"',

Members of the Technical Committee during the preparation of this report were:

P J. Alessi

USA

EC. Carter

USA

M.D. Fairchild

USA

R.W.G. Hunt

United Kingdom

C.S. McCamy

USA

B. Kranicz

Hungary

J.R. Moore

United Kingdom

L. Morren

Belgium

J.H. Nobbs

United Kingdom

Y. Ohno

USA

M.R. Pointer

United Kingdom

D.C. Rich

USA

A.R. Robertson

Canada

J.D. Schanda (chair)

Hungary

R. Seve

France

P.W. Trezona

United Kingdom

K.Witt

Germany

H. Yaguchi

Japan

The following Editorial Committee was responsible for the formulation of the document: E.C.
Carter, Y. Ohno, M.R. Pointer, A.R. Robertson, R. Seve, J.D. Schanda, K. Witt.

Items of mainly historic importance have been placed into Appendix A.

According to the new CIE publication numbering policy - that indicates a new revised edition
only by the year of publication - this technical report has got the number of 15:2004 and not
15.3:2004.

Ill

CIE 15:2004

TABLE OF CONTENTS

SUMMARY VII

RESUME VII

ZUSAMMENFASSUNG VII

1. SCOPE 1

2. PREFACE 1

3. RECOMMENDATIONS CONCERNING STANDARD PHYSICAL DATA OF
ILLUMINANTS AND SOURCES 2

3.1 Recommendations concerning standard physical data of illuminants 2

3.2 Artificial sources representative of illuminants 5

4. RECOMMENDATIONS CONCERNING STANDARD OF REFLECTANCE 5

5. RECOMMENDATIONS CONCERNING GEOMETRIC CONDITIONS FOR
COLORIMETRY 5

5.1 Recommended nomenclature for directional irradiation 6

5.1.1 Forty-five degree directional geometry (45°x) 6

5.1.2 Forty-five degree annular geometry (45°a) 6

5.1.3 Zero degree directional geometry (0°) 6

5. 1 .4 Eight degree geometry (8°) 7

5.2 Recommended geometry for reflection measurements 7

5.2.1 Diffuse: eight-degree geometry, specular component included (di:8°) 7

5.2.2 Diffuse: eight-degree geometry, specular component excluded (de:8°) 7

5.2.3 Eight degree: diffuse geometry, specular component included (8°:di) 7

5.2.4 Eight degree: diffuse geometry, specular component excluded (8°:de) 7

5.2.5 Diffuse /diffuse geometry (d:d) 7

5.2.6 Alternative diffuse geometry (d:0°) 7

5.2.7 Forty-five degree annular / normal geometry (45°a:0°) 7

5.2.8 Normal / forty-five degree annular geometry (0°:45°a) 8

5.2.9 Forty-five degree directional / normal geometry (45°x:0°) 8

5.2.10 Normal / forty-five degree directional geometry (0°:45°x) 8

5.3 Recommended geometry for transmission measurements 8

5.3.1 Normal / normal geometry (0°:0°) 8

5.3.2 Diffuse / normal geometry, regular component included (di:0°) 9

5.3.3 Diffuse / normal geometry, regular component excluded (de:0°) 9

5.3.4 Normal / diffuse geometry, regular component included (0°:di) 9

5.3.5 Normal / diffuse geometry, regular component excluded (0°:de) 9

5.3.6 Diffuse / diffuse geometry (d:d) 9

6. RECOMMENDATIONS CONCERNING STANDARD OBSERVER DATA 9

6.1 CIE 1931 standard coiorimetric observer 9

6.2 CIE 1964 standard coiorimetric observer 10

7. RECOMMENDATIONS CONCERNING THE CALCULATION OF TRISTIMULUS
VALUES AND CHROMATICITY COORDINATES 12

7.1 Calculation of tristimulus values 12

7.1.1 Secondary light sources (reflecting or transmitting objects) 1 2

7.1.2 Illuminants and self-luminous objects 13

7.2 The use of abridged or truncated data 1 3

7.2.1 Abridgement 13

7.2.2 Truncation 14

7.2.3 Weighting factors 14

7.2.4 Numerical procedures 15

7.2.5 Bandwidth of a spectrometer 15

7.3 Calculation of chrornaticity coordinates 15

7.4 Equations representing relationships between colour stimuli 16

IV

CIE 15:2004

8. RECOMMENDATIONS CONCERNING UNIFORM COLOUR SPACING AND

COLOUR DIFFERENCES 16

8.1 CIE 1976 uniform chromaticity scale diagram (UCS diagram) 16

8.2 CIE 1976 uniform colour spaces 16

8.2.1 CIE 1976 (L*a*b*) colour space; CIELAB colour space 17

8.2.2 CIE 1976 (L*u*v*) colour space; CiELUV colour space 18

8.2.3 Notes on CIE 1976 uniform colour spaces 19

8.3 Improved industrial colour difference evaluation 20
8.3.1 C1EDE2000 total colour difference formula 20

9 RECOMMENDATIONS CONCERNING MISCELLANEOUS COLORIMETRIC

PRACTICES AND FORMULAE 22

9.1 Dominant wavelength and purity 22

9.1.1 Dominant wavelength (of a colour stimulus), X d 22

9.1.2 Complementary wavelength (of a colour stimulus), X c 22

9.1.3 Colorimetric purity, p c 22

9.1.4 Excitation purity, p e 22

9.2 Special metamerism indices 23

9.2.1 Special metamerism index: change in illuminant 23

9.2.2 Special metamerism index: change in observer 24

9.3 Assessment of the quality of a daylight simulator for colorimetry 25

9.4 The evaluation of whiteness 26

9.5 Calculation of correlated colour temperature 26

10. REFERENCES 27

11. TABLES 30
11.1 Table T.1. Relative spectral power distributions of CIE illuminants 30
11. 2 Table T.2. Components S (2), Si(A), S^X) 33
1 1.3 Table T. 3. Tristimulus values, chromaticity coordinates of CIE illuminants 35
11.4TableT.4. CIE 1931 standard colorimetric observer 36
11.5TableT.5. CIE 1964 standard colorimetric observer 38
1 1 .6 Table T.6. Relative spectral power distributions of illuminants representing typical

fluorescent lamps, for wavelengths X = 380 nm to 780 nm at 5 nm intervals 40

11.7 Table T.7. High pressure discharge lamps. HP1: Standard high pressure sodium
lamp; HP2: Colour enhanced high pressure sodium lamp; HP3-5: Three types of
high pressure metai halide lamps 47

11.8 Table T.8. Colorimetric data for the fluorescent lamp illuminants of Table T.6 49

1 1.9 Table T.9. Colorimetric data for the high pressure illuminants of Table T.7 50

1 1 .10 Table T.10. Values of the first deviation function used in the calculation of the
observer metamerism index 51

APPENDIX A. OLD RECOMMENDATIONS, NOW OBSOLETE, AS WELL AS

REFERENCES TO NON-CIE COLOUR DIFFERENCE FORMULAE 52

Appendix A. 1 . Illuminant B and Source B 52

Appendix A.2. Illuminant C and Source C 52

Appendix A.3. CIE 1964 uniform colour space and colour difference formula 53

u, v uniform chromaticity scale (CIE 1960 UCS) diagram 53

1964 uniform space and colour difference formula 53

Appendix A.4. CIE 1994 colour difference formula (CIE94) 53

Appendix A.5. CMC(i:c) colour difference formula 54

Appendix A. 6. DIN99 colour difference formula 54

References 54

APPENDIX B. DEFINITIONS OF THE 7(X\g(X)MX) COLOUR-MATCHING

FUNCTIONS, THE CIE RGB SYSTEM AND THE DERIVATION OF THE CIE XYZ
SYSTEM FROM THE CIE RGB SYSTEM FOR THE 1931 STANDARD OBSERVER 55

Appendix B.1. Determination of the r{X) 1 g(X),b(X) colour-matching functions 55

Appendix B.2. Derivation of the CIE XYZ trichromatic system from the CIE RGB

trichromatic system 56

V

CIE 15:2004

Appendix B.3. Definition of the colour-matching functions in the CIE 1964 trichromatic

system 57

Reference 61

APPENDIX C. ALTERNATIVE METHOD TO DEFINE DAYLIGHT ILLUMINANTS -
METHOD OF CALCULATION, CORRECTED TABLES AND EQUATIONS (FOR
INFORMATION AND EVALUATION) 62

References 65

APPENDIX D. REVERSE TRANSFORMATION FROM VALUES L*. a*, b* TO

TRISTIMULUS VALUES X, Y, Z 66

Reference 66

APPENDIX E. INFORMATION ON THE USE OF PLANCK'S EQUATION FOR

STANDARD AIR 67

References 67

EXPLANATORY COMMENTS 68

Vi

CI E 15:2004

COLORIMETRY

SUMMARY

This publication provides the recommendations of the CIE concerning basic coiorimetry.
Specifically, it includes the use of the standard illuminants and the standard colorimetric
observers; the reference standard for reflectance; the illuminating and viewing conditions; the
calculation of tristimulus values, chromaticity coordinates, colour spaces and colour
differences; and the various other colorimetric practices and formulae.

This publication is consistent with the fundamental data and procedures described in
the CIE Standards on Coiorimetry.

For further details of some of the phenomena discussed here the reader is directed to
the appropriate technica! reports.

COLORIMETRIE

RESUME

Ce document donne ies recommandations de la CIE pour la colorimetrie de base. Plus
particulierement il traite de I'emploi des illuminants normalises et des observateurs
colorimetriques normalises, de la reference normaiisee pour le facteur de reflexion, des
conditions d'eclairage et d'observation, du calcul des composantes trichromatiques, des
coordonnees trichromatiques, des espaces chromatiques et des ecarts de couleur, ainsi que
de i'emploi de diverses autres pratiques et formules colorimetriques.

Cette publication est en accord avec ies donnees et procedures de base qui sont
decrites dans Ies normes CIE de colorimetrie.

Pour des details complementaires relatifs aux questions traitees ici, le lecteur est
invite a consulter Ies rapports techniques appropries.

FARBMESSUNG

ZUSAMMENFASSUNG

Die hier wiedergegebenen Empfehlungen der CIE beziehen sich auf die Anwendung Oder die
Benutzung der Normlichtarten und der Normalbeobachter, auf den WeiGstandard, auf die
Beleuchtungs- und Beobachtungsbedingungen, auf die Berechnung von Normfarbwerten und
Normfarbwertanteilen, FarbenrSumen und Farbabstanden, und auf verschiedene andere
farbmetrische Praktiken und Formeln.

Diese Veroffentlichung stimmt mit den grundlegenden Daten und Verfahren uberein,
die in CIE Normen fur Farbmessung beschrieben sind.

Weitere Einzelheiten einiger hier dsskutierter Phanomene findet der Leser in
geeigneten technischen Berichten.

VII

C!E 15:2004

VIII

CiE 15:2004

1. SCOPE

This report is intended to provide a consistent and comprehensive account of the
recommendations of the CIE for basic colorimetry. It summarises basic colorimetric data and
practices; it does not, however, deal with colour appearance specification.

2. PREFACE

By general consent in all countries the specification of basic standards for use in colorimetry
is the province of the Commission Internationale de I'Eclairage (CIE). The first major
recommendations regarding colorimetric standards were made by the CIE in 1931, and these
formed the basis of modern colorimetry. The original recommendations of 1931 were
reviewed from time to time by the CIE Colorimetry Committee and later by CIE Division 1,
Vision and Colour When necessary changes were made. New recommendations were
added to supplement the existing ones or to broaden the scope of colorimetry in accordance
with developments in practice and science.

The deliberations and recommendations made by the CIE Colorimetry Committee
and Division 1 are recorded in the Proceedings of the various Sessions of the CIE. However
the access to these Proceedings has always been rather limited and much of the material
published in the Proceedings is obsolete or inconsistent with current colorimetric practice.
The recommendations, while few in number, also present an incoherent picture. Many
recommendations are merely proposals of study or work on certain topics that were
considered important at the time.

For these reasons in 1971 the CIE published a special document on colorimetry to
provide a consistent and comprehensive account of basic colorimetric recommendations.
This document was not intended to be a textbook on colorimetry but rather a reference to the
basic standards that govern modern colorimetry. The document was issued as CIE
Publication No. 15 (CIE, 1971).

Since 1971 it has been necessary to add two supplements to the document [Suppl. 1
on Special metamerism index: change of iliuminant (CIE, 1972) and Suppl. 2 on
Recommendations on uniform colour spaces, colour-difference equations and psychometric
colour terms (CIE, 1978)]. Several Technical Reports were also published during the
intervening years. Publication CIE 15.2, published in 1986 (CIE, 1986b) incorporated the first
two supplements. Further amendments, described in detail in CIE 51-1981, A method for
assessing the quality of daylight simulators for colorimetry (CIE, 1981); CIE 80-1989, Special
metamerism index: observer metamerism (CIE, 1989); CIE 101-1993, Parametric effects in
colour difference evaluation (CIE, 1993); CiE 116-1995, Industrial colour difference evaluation
(CIE, 1995a); CiE 135/3, CIE TC 1-45 report: Supplement 1-1999 to CIE 51-1981, Virtual
metamers for assessing the quality of simulators of CIE iliuminant D50 (CIE, 1999b) and CIE
142-2001 , Improvement to industrial colour difference evaluation (CIE, 2001a) are all parts of
the CiE system of colorimetry. The present version, CIE 15:2004 summarises all CIE
recommendations on basic colorimetry. Short explanatory texts and a historic overview are
also included. Colour appearance models are not covered, for these see CiE 131-1998 (CIE,
1998a); CIE 159:2004 (CIE, 2004b) and CIE X014-1998 (CIE, 1998b).

In compiling this third edition the opportunity has been taken to incorporate all
relevant recommendations. The publications enumerated in the previous paragraph contain
background information on the single subjects, those interested in more detail about the
development of the recommendations and their background experiments are referred to these
publications. CIE 15:2004 is based on CIE standards containing the fundamental data on CIE
standard illuminants and standard observers. The presently official versions of these
standards are CIE S 005-1998, CIE standard illuminants for colorimetry (CIE, 1998c)
(published also as ISO 10526:1999) and CIE S 002-1986, CIE standard colorimetric
observers (CIE, 1986a), (published also as CIE/ISO 10527:1991). These standards contain
the fundamental colorimetric data [see also CIE DS 014-2.2:2004 (CIE, 2004a)].

It is anticipated that further amendments of colorimetric practice and further
standards will be published, thus one should consult the latest CIE list of publications
published in CIE Proceedings, and in most recent Technical Reports; this information is also
available on the CIE world wide web home page (http://www.cie.co.at/).

CIE 15:2004

The wording of the original recommendations has been altered to be consistent with
modern nomenclature and in some cases the original recommendations have also been
modified in content to bring them into line with present day thinking and practice. The
versions given in this document are the recommendations now in force and supersede all
previous recommendations until such time as any amendments are published by the CIE.

The recommendations are divided into the following seven groups:

- Recommendations concerning standard physical data of illuminants and sources.

- Recommendations concerning the standard of reflectance.

- Recommendations concerning geometric conditions for colorimetry.

- Recommendations concerning standard observer data.

- Recommendations concerning the calculation of tristimulus values and chromaticity
coordinates.

- Recommendations concerning uniform colour spacing and colour difference.

- Recommendations concerning miscellaneous colorimetric practices and formulae.

The definitive data relating to standard colorimetric illuminants and observers are
those given at 1 nm intervals in the appropriate CIE standards [CIE, 1998c (to be replaced by
CIE, 2004a); CIE, 1986a]. The data have not been printed in the present report, but are
included in the accompanying CD-ROM. Abridged data, at 5 nm intervals, are given in
Section 11, and these may be used in those cases where calculation at the wider intervals is
unlikely to produce any significant error.

For ali colorimetric calculations wavelength in standard air should be used l! \

3. RECOMMENDATIONS CONCERNING STANDARD PHYSICAL DATA OF

ILLUMINANTS AND SOURCES

3.1 Recommendations concerning standard physical data of illuminants 2

It is recommended that the following illuminants, defined by relative spectral power
distributions given in Table 1 of CIE S 005-1998 (CIE, 1998c) m , be used for general
colorimetry.

• CIE standard illuminant A

The relative spectral power distribution S A (A) is defined by the equation

1,435x10 7 A
ex p 1

jfSGOY '2848x560

S A (2) = 100 — x 7 (3-1)

A { A J 1,435x10 7 „

exp 1

2 848/1

where A is the wavelength in nanometres and the numerical values in the two exponential
terms are definitive constants originating from the first definition of Illuminant A in 1931 3 . This
spectral power distribution is normalized to the value 100 (exactly) at the wavelength 560 nm
(exactly).

CIE standard illuminant A is defined over the spectral region from 300 nm to 830 nm iV
in CIE S 005-1998 (CIE, 1998c) to six significant digits. Should higher precision be needed,

!t Superscripts of Arabic numerals refer to Explanatory Comments given on page 68-72.

! " The spectral power distribution tables published in the CIE Standard are reproduced on the
CD-ROM that accompanies this Technical Report.

!V The wavelength range for standard illuminants is 300 nm - 830 nm because, for evaluating
luminescent samples the UV spectral range is relevant. For most colorimetric investigations
the restricted wavelength range, 380 nm - 780 nm, can be used.

CI E 15:2004

values calculated using Equ 3.1 should be used v Section 11 contains abridged tables that
can be used in most practical calculations. On the use of these tables see Section 7.2.

Note 1: The definition reproduced here is in accordance with the values of iliuminant A
originally published in 1931, see CIE S 005-1998 (CIE, 1998c) and CIE DS014-
2.2:2004 (CIE, 2004a).

Note 2: Despite the fact that Equ. 3.1 is based on Planck's equation for a vacuum, the
wavelengths are to be taken as being in standard air (dry air at 15°C and 101325 Pa,
containing 0,03% by volume of carbon dioxide). This makes CIE standard iliuminant A
compatible with other CIE colorimetric and photometric data.

« CIE standard iliuminant D65

The relative spectral power distribution representing a phase of daylight with a correlated
colour temperature of approximately 6500 K (called also nominal correlated colour
temperature of the daylight iliuminant) 4 , symbol: S D65 (i). The official values of S D65 (/i) are as
given in CIE standard illuminants for colorimetry (CIE, 1998c) vl .

Note 1: Regarding the definition of correlated colour temperature (T" cp ) of an iliuminant see
Section 9.5.

Note 2: Section 11 provides abridged tables that can be used in many practical calculations.
On the use of these tables see Section 7.2. The values of relative spectral power
distribution of CIE standard iliuminant D65 given in Table T.1 at 5 nm intervals are
consistent with the values from 300 nm to 830 nm at 1 nm intervals and with six
significant figures given in CIE standard illuminants for colorimetry (CIE, 1998c). They
have been taken from the tables of the Standard.

Note 3: If values at other wavelengths than printed in Table 1 of the standard (CIE, 1998c) at
1 nm intervals are needed, linear interpolation should be used.

• Other illuminants D

It is recommended that, in the interest of standardization, D65 be used whenever possible.
When D65 cannot be used, it is recommended that one of the daylight illuminants D50, D55,
or D75 defined in Table T.1 be used. When none of these daylight illuminants can be used, a
daylight iliuminant at a nominal correlated colour temperature (T cp ) can be calculated using
the following equations. These equations will give an iliuminant whose correlated colour
temperature is approximately equal to the nominal value, but not exactly so 4 .

(a) Chromaticity

The 1931 (x,y) chromaticity coordinates of the daylight (D) to be defined must satisfy the
following relation:

y D = -3,000x D 2 + 2 t 870x D - 0,275 (3.2)

with x D being within the range of 0,250 to 0,380. The correlated colour temperature 7 cp of
daylight D is related to x D by the following formulae based on normals to the Planckian locus
on a uniform chromaticity diagram (see Section 9.5):

(i) for correlated colour temperatures from approximately 4000 K to 7000 K:
-4,6070x10 9 2,9678x10 6 0,09911x10 3 nr%AAnnrt

Xo ' u f "s cr* 0244061 (3 - 3)

(ii) for correlated colour temperatures from greater than 7000 K to approximately 25 000 K:

v Terminology in this publication follows the traditional terminology used in colorimetry. A
separate publication on colorimetry will deal with the current "uncertainty" description of
stating measurement results and will recommend methods for calculating colorimetric
uncertainties.

Vl The spectral power distribution tables published in the CIE Standard are reproduced on the
CD-ROM that accompanies this Technical Report.

CIE 15:2004

-2,0064x10 9 1,9018x10 6 0,24748x10 3 n ^ nAn ,_

x °=^j — u — ^ +w3?o4 ° <34 »

(b) Relative spectral power distribution

The relative spectral power distribution S(A) of daylight D is to be computed from

S(Xj = S (A) + M,S,(A) + M 2 S 2 (1) (3.5)

where S (A), S^Xj, S Z U) are functions of wavelength, A, given in Table T.2, and M u M 2 are
factors whose values are related to the chromaticity coordinates x Dl y D as follows:

M - " 1 . 3515 -V 703x d +5,9114y D
1 ~ 0,0241 + 0,256 2x D - 0,734 1y D

(3.6)
_ 0,0300 -31,44 24x D +30,0717y D

0,024 1 + 0,256 2x D - 0,734 1y D

Notes on standard illuminant D65 and other illuminants D

Note 1: Seasonal and geographical variations in the spectral power distribution of daylight
occur, particularly in the ultraviolet spectral region, but this recommendation should
be used pending the availability of further information on these variations.

Note 2: The spectral power distributions of daylight illuminants D produced by this
recommendation are based on experimental observations over the wavelength range
330 nm to 700 nm, and on extrapolation in the wavelength ranges 300 nm to 330 nm
and 700 nm to 830 nm (see Judd et al., 1964). The extrapolated values are believed
to be accurate enough for colorimetric purposes, but should not be used for other
purposes.

Note 3: If values at other wavelengths than those printed in Table T.2 are needed, linear
interpolation should be used (see also Appendix C).

Note 4: The relative spectral power distributions of the D illuminants given in Table T.1 and in
the CIE standard on illuminants for colorimetry (CIE, 1998c) were derived by the
procedure given above with some intermediate rounding and with some adjustments
for changes in the International Temperature Scale 5 . Thus for historic reasons, the
tabulated values are slightly different from the calculated values. For the time being
the tabulated values are the official data. (Eventually these data may be superseded
by the method described in Appendix C, which provides a harmonised method of
calculation for trial that will produce congruent results if the modified tables and
equations are used.)

Note 5: When samples exhibiting luminescence excited by ultraviolet radiation are involved,
one of the D illuminants defined in these recommendations should always be used to
represent daylight.

« Illuminant B

Intended to represent direct sunlight with a correlated colour temperature of approximately
4900 K.

Note: The use of this illuminant is deprecated, see Appendix A.

9 Illuminant C

Intended to represent average daylight with a correlated colour temperature of approximately
6800 K.

Note 1 : Illuminant C does not have the status of a CIE standard but its relative spectral power
distribution, tristimulus values and chromaticity coordinates are given in Table T.1
and Table T.3, as many practical measurement instruments and calculations still use
this illuminant.

Note 2: The tristimulus values and chromaticity coordinates of the illuminant C and of D50,

CI E 15:2004

D55, D75, calculated from the values of S(A), given in Table T.2., are shown in Table
T.3. The reproduced tristimulus values are those of the perfect reflecting diffuser
irradiated by the respective illuminant, see Section 7.1.1 This table also includes
similar data for C1E standard illuminant A and D65.

3.2 Artificial sources representative of illuminants

It is recommended that the following artificial sources be used if it is desired to realise the
illuminants defined in Section 3.1 for actual laboratory inspection.

• Source A

CIE standard illuminant A is to be realised by a gas-filled tungsten filament lamp operating at
a correlated colour temperature of 2856 K (c 2 = 1, 4388x1 0' 2 m-K). If the source is also to be
used in the UV region, a lamp having an envelope or window made of fused-quartz or silica
must be used because glass absorbs the UV component of the radiation from the filament,

• Source B

See Appendix A.

• Source C

See Appendix A.

o Source D65

At present no artificial source is recommended to realise CIE standard illuminant D65 or any
other illuminant D of different correlated colour temperature. It is hoped that new
developments in light sources and filters will eventually offer sufficient basis for a CIE
recommendation. Meanwhile the CIE has agreed on a formula to describe the quality of a
daylight simulator for colorimetry, see Section 9.3.

Notes on artificial sources representative of illuminants

Note 1: The artificial sources defined above and recommended as representative sources for
CIE illuminants are named "CIE sources for coiorimetry".

Note 2: Whenever the highest accuracy of the spectral power distribution of a standard is
required, it is advisable to make a spectroradiometric calibration of the actual source
used, because the relative spectral power distribution of the source may not exactly
coincide at all wavelengths with that defining the corresponding illuminant.

Note 3: The spectrum of a D65 simulator fluorescent lamp is reproduced in Table T.6.2b as
FL3.15, see Section 9.3.

4. RECOMMENDATIONS CONCERNING STANDARD OF REFLECTANCE 6

The perfect reflecting diffuser is the reference standard for reflectance (CIE, 1986a). It is
defined as the ideal isotropic diffuser with a reflectance equal to unity. For real
measurements, reflectance standards, such as pressed barium sulphate or PTFE (known
also under the trade names Algoflon, Halon, Spectraion), must be calibrated in terms of the
perfect reflecting diffuser (see CIE, 1979a; CIE, 1979b) for the required geometry.

5. RECOMMENDATIONS CONCERNING GEOMETRIC CONDITIONS FOR

COLORIMETRY 7

Coiorimetric specifications are derived from spectral or tristimulus measurements. The
measured values depend on the geometric relationships between the measuring instrument
and the sample. These relationships are called "geometric conditions" or simply "geometry".
Similarly, visual appraisals of coloured samples are affected by illuminating and viewing
geometry. The degree of correlation between measured values and visual appraisals
depends on the degree to which the geometric conditions of measurement simulate the
geometric conditions of viewing. (The use of the term "viewing" with reference to measuring

CIE 15:2004

instruments is deprecated because it blurs the important distinction between instrumental
measurements and visual observation.)

Terms and definitions used in this Section of CIE 15:2004 introduce a terminology not
used in previous versions of CIE 15, they are the following:

reference plane

plane in which the surface of a sample or standard is placed during measurements
For reflection measurements, the geometry is defined with respect to the reference
plane. For transmission measurements, there is a reference plane for the incident
light and a second reference plane, displaced by the sample thickness, for the
transmitted light. The recommendations of this publication are based on the
assumption of negligible thickness.

sampling aperture

area of the reference plane on which measurements are made
The sampling aperture is delimited by the area illuminated or by the area over which
the receiver senses flux, whichever is smaller. If the illuminated area is the larger, the
area measured is said to be "over filled"; if it is the smaller, the area measured is said
to be "under filled".

modulation

generic term for measured ratios such as reflectance, reflectance factor or
transmittance

irradiation or influx (illumination or incidence) geometry

angular distribution of irradiance at the centre of the sampling aperture

reflection/transmission or efflux (collection, measuring) geometry

angular distribution of receiver responsivity with respect to the centre of the sampling
aperture

Note: The influx and efflux geometry specify the geometric nature of the measurement.

It is recommended that the geometry used when determining the colorimetric
specification of diffusely reflecting samples corresponds to one of the following irradiating
(influx) and reflection/transmission (efflux) conditions Vli .

5.1 Recommended nomenclature for directional irradiation

5.1.1 Forty-five degree directional geometry (45° x)

Irradiation of reflecting materials at 45° to the normal, at one azimuth angle, emphasizes
texture and directionality. The "x" in the symbol indicates that the azimuthal direction of the
incident beam is in the x direction on the reference plane.

5.1.2 Forty-five degree annular geometry (45° a)

In measuring the colours of reflecting samples with 45° illumination, the effects of texture and
directionality are minimized by irradiating at 45° to the normal, from all azimuthal directions,
simultaneously. This irradiation (influx) geometry may be achieved by the use of a small
source and an elliptic ring reflector or other aspheric optics. This geometry is sometimes
approximated by the use of a number of light sources in a ring or a number of fibre bundles
illuminated by a single source and terminated in a ring. Such an approximation to annular
geometry is called circumferential geometry, symbol 45°c.

5. 1.3 Zero degree directional geometry (0°)
Irradiation of reflecting materials at the normal.

VM Users of this report should check with the CiE list of publications for a technical report on
this subject.

CiE 15:2004

5.1.4 Eight degree geometry (8°)

Irradiation of reflecting materials at 8° to the normal, at one azimuth angle. It is used to
substitute the zero-degree directional geometry in many practical applications, as in reflection
measurements it permits differentiation between specular component included and excluded
measurements.

5.2 Recommended geometry for reflection measurements

5.2. 1 Diffuse: eight-degree geometry, specular component included (di:8°)

For di:8° geometry, it is recommended that the sample be irradiated by an integrating
sphere 8 , that the measured area be overfilled, that the area of the sampling aperture be
uniformly irradiated, that it be irradiated uniformly from all directions within the hemisphere
bounded by its plane, that the responsivity of the receiver be uniform over the area of the
sampling aperture, that the axis of the reflected (efflux) beam be 8° off the normal to the
centre of the sample, and that radiation reflected at the sampling aperture be evaluated
uniformly at all directions within 5° of the axis of the collection (efflux) beam. The size of the
sampling aperture, area and angular uniformity of irradiation, angular displacement of the
collected (efflux) beam from the normal, and area and angular uniformity of responsivity of the
receiver can affect measured values and may be standardized in the future.

5.2.2 Diffuse: eight-degree geometry, specular component excluded (de:8°)

It is recommended that the specifications for di:8° be met, except that there be no radiation
reflected in the direction of the receiver by a plane first-surface mirror at the sampling
aperture and that there be no rays specularly reflected within 1° of such rays, as an allowance
for instrumental scattering of stray light or misalignment. The amount of stray light specularly
reflected in the direction of the receiver may affect measured values and may be
standardized in the future.

5.2.3 Eight degree: diffuse geometry, specular component included (8°:di)

It is recommended that the conditions for di:8° be met, but with the light path reversed, so the
sampling aperture is irradiated under 8° and flux reflected at the sampling aperture is
collected at all angles in the hemisphere bounded by the reference plane. The sampling
aperture should be underfilled with radiation.

5.2.4 Eight degree: diffuse geometry, specular component excluded (8°:de)

It is recommended that the geometric conditions for de:8° be met, but with the light path
reversed. The sampling aperture should be underfilled with radiation.

5.2.5 Diffuse / diffuse geometry (d:d)

It is recommended that for irradiation the specifications for di:8° be met, and flux reflected at
the sampling aperture is collected at all angles in the hemisphere bounded by the reference
plane. In this geometry the sampling aperture can be neither underfilled nor overfilled.

5. 2. 6 Alternative diffuse geometry (d:0°)

An alternative diffuse geometry is the strict specular excluded geometry defined when the
efflux direction is along the specimen normal.

5.2. 7 Forty-five degree annular/ normal geometry (45°a:0°)

It is recommended that the sampling aperture be irradiated uniformly from all directions
between two right circular cones with their axes on the normal to the sampling aperture and
apices at the centre of the sampling aperture, the smaller cone having a half angle of 40° and
the larger of 50°. It is recommended that the receiver uniformly collects and evaluates all
radiation reflected within a cone with its axis on the normal to the sampling aperture, apex at
the centre of the sampling aperture, and a half angle of 5°. If this illuminating geometry is
approximated by the use of a number of light sources in a ring or a number of fibre bundles
illuminated by a single source and terminated in a ring, one gets the circumferential / normal

CIE 15:2004

geometry (45°c:0°). The above angular specifications should also hold for this geometry.
These angular specifications and the surface and angular uniformity of irradiation and sensing
may affect measured values and may be standardized in the future.

5.2.8 Normal / forty-five degree annular geometry (0°:45°a)

It is recommended that the angular and spatial conditions for 45°a:0° be met, with the light
path reversed, so the sampling aperture is irradiated normally and reflected radiation is
collected within an annulus centred at 45° to the normal.

5. 2. 9 Forty-five degree directional / normal geometry (45°x:0°)

It is recommended that the angular and spatial conditions for 45°a:0° be met with the
exception that irradiation is only at one azimuth angle, this excludes the specular component,
but emphasizes texture and directionality. The "x M in the symbol indicates that the azimuthal
direction of the incident beam is in the x direction on the reference plane,

5.2. 10 Normal / forty-Five degree directional geometry (0°:45°x)

It is recommended that the angular and spatial conditions for 45°x:0° be met, with the light
path reversed, so the sampling aperture is irradiated normally and reflected radiation is
collected at one azimuth angle at 45° to the normal.

Notes on recommended geometry for reflection measurements

Note 1: Conditions 5.2.1, 5.2.2, 5.2.6, 5.2.7, 5.2.8, 5.2.9 and 5.2.10 give values of reflectance
factor, R(A). For directional measurement with a sufficiently small angular spread,
these values of reflectance factor become identical to values of radiance factor. For
condition 5.2.3, for measuring with an ideal sphere, reflectance is measured. Thus, in
the limit, the 45°x:0° condition gives the radiance factor f] 450 \ the 0°:45°x condition
gives the radiance factor yft^; the di:8° condition gives the factor /? di:8 ; that
approximates the radiance factor /? d . ; and the 8°:di condition gives the reflectance p
(see CIE, 1987).

Note 2: It is important that the particular irradiating and measuring conditions used should be
specified even if they are within the range of one of these recommended standard
conditions. Measurements of some types of samples (for example retro-reflective
materials) may require different geometry or tolerances.

Note 3: When integrating spheres are used, they should be fitted with white-coated baffles to
prevent light passing directly between the sample and the spot of the sphere wall
irradiated or measured. When the regular component of reflection is to be included,
the sphere efficiency for that part of sphere wall that receives the regularly reflected
radiation component should be of the same reflectance value as the sphere wall. The
total area of the ports of the integrating sphere should not exceed 10 percent of the
internal reflecting sphere area.

Note 4: It should be noted that diffusing samples may scatter radiation in directions
approximately parallel to their surfaces, and such radiation should be included in the
measurement of diffuse reflectance.

Note 5: When integrating spheres are used for measuring luminescent samples, the spectral
power distribution of the irradiating system is altered by the reflected and emitted
power from the sample (see CIE, 1988). The use of the 45°a:0°, 45°x:0° or 0°:45°a,
0°:45°x condition is therefore preferable (see Gundlach and Mallwitz, 1976; Alman
and BiSlmeyer, 1976).

5.3 Recommended geometry for transmission measurements

5.3.1 Normal / normal geometry (0°:0°)

It is recommended that the irradiating (influx) and measuring (efflux) geometry be of identical
right-circular conic form, with their axes on the normal to the centre of the sampling aperture,
and half-angle of 5°, that the surface and angular irradiation of the sampling aperture be

CIE 15:2004

uniform, and that the surface and angular responsivity of the receiver be uniform. Deviation of
axes from normal and variations in surface and angular conditions may affect measured
values and may be standardized in the future.

5.3.2 Diffuse / normal geometry, regular component included (di:0 °)

It is recommended that the sampling aperture be uniformly irradiated from all directions in the
hemisphere bounded by the first reference plane and that the measuring (efflux) beam be as
specified for 0°:0° geometry. Deviation of the measuring (efflux) axis from normal and
variations in surface and angular conditions may affect measured values and may be
standardized in the future.

5. 3. 3 Diffuse / normal geometry, regular component excluded (de:0°)

It is recommended that the geometry be that specified for di:0° except that, with the sampling
aperture open (i.e. no sample in place), there be no rays directed toward the receiver and no
rays within 1° of such rays, as measured at the centre of the sampling aperture.

5.3.4 Normal / diffuse geometry, regular component included (0°:di)

It is recommended that the geometry be the reverse of that specified for di:0° geometry.

5.3.5 Normal / diffuse geometry, regular component excluded (0 °:de)

It is recommended that the geometry be the reverse of that specified for de:0° geometry.

5. 3. 6 Diffuse / diffuse geometry (d:d)

It is recommended that the sampling aperture be uniformly irradiated at all angles within the
hemisphere bounded by the first reference plane and that the transmitted flux be uniformly
evaluated at ail directions within the hemisphere bounded by the second reference plane.

Notes on recommended geometry for transmission measurements

Note 1: All the above conditions measure transmittance except for those where the regular
component is excluded when the quantity measured is transmittance factor.

Note 2: It is important that the particular irradiating and collecting conditions used are specified,
even if they are within the range of one of the conditions recommended here.
Measurements of some types of samples may require different geometry or tolerances.

Note 3: Integrating spheres shall be fitted with white-coated baffles to prevent radiation
passing directly from source to sample or reference in the case of diffuse irradiation
or directly from sample or reference to detector in the case of diffuse collection. The
total area of the ports of the integrating sphere should not exceed 10 percent of the
internal reflecting sphere area.

Note 4: The construction of an instrument for normal/normal measurements shall be such that
the irradiating (influx) and collecting (efflux) beams shall be equal whether there is a
sample in place or not.

Note 5: It should be noted that diffusing samples may scatter radiation in directions
approximately parallel to their surfaces, and such radiation should be included in the
measurement of diffuse transmittance.

Note 6: Multiple reflections between the sample and the incident beam optics if the incident
beam is normal to the sample surface may cause measurement errors. These can be
eliminated by slightly tilting the sample.

6. RECOMMENDATIONS CONCERNING STANDARD OBSERVER DATA 9

6.1 CIE 1931 standard colorimetric observer

For correlation with visual colour matching of fields subtending between about 1° and about
4° at the eye of the observer, it is recommended that colorimetric specifications of colour

CIE 15:2004

stimuli be based on the colour-matching functions x(A), y{X\ z(/l) 10 . A 2° visual field

represents a diameter of about 17 mm at a viewing distance of 0,5 m. These colour-matching
functions are given in the standard as values from 360 nm to 830 nm at 1 nm intervals with
seven significant figures, and they define the CIE 1931 standard colorimetric observer (in
technical applications often written as 2°-standard colorimetric observer) vll! . In the case where
more coarsely sampled data will produce no significant calculation error, the tables
reproduced in Section 1 1 may be used instead of the 1 nm interval data. The values given in
Table T.4 at 5 nm intervals are selected values from the standard, rounded to six decimal
places 11 .

Note 1: x(A), y(A), z(X) are the normalized tristimulus values of monochromatic radiations for
a set of reference stimuli [X], [Y], [Z] required to match each wavelength of the equi-
energy spectrum. Their levels are such that the maximum of y(A)is unity and Ex(A)

= lz(X) = Sy(2). (The equi-energy spectrum is radiation whose spectral
concentration of power as a function of wavelength is constant.)

Note 2: The real reference stimuli [R], [G], [B] of the original trichromatic system lead, by
transformation, to [X], [Y], [Z]. y(X) is equated to V{X), the spectral luminous efficiency

function for photopic vision, defining the CiE standard photometric observer for
photopic vision (for more details see Appendix B).

Note 3: The reference stimuli [X], [Y], [Z] were chosen for reasons of convenience in
colorimetric computations. The colour-matching functions x(X) , y(X), z(X) are
commonly used to obtain the tristimulus values X, Y, Z of colour stimuli (see Section
7.1 for details).

Note 4: If the colour-matching functions at closer intervals than given in Table T.4 are required,
the values given in the CIE Standard S002 (CiE, 1986a) should be used. For
interpolation at wavelength intervals smaller than 1 nm a linear interpolation should be
used.

Note 5: The chromaticity coordinates (see Section 7.3) x{X), y{A), z(X) of the spectral stimuli
are the ratios

x(A) + y(X) + I(X)

y (X) = ^ 1^ _ (6.1)

x(A) + y(X) + z(X)

x(X) + y(X) + z(X)

x(X) and y(X) are given in Table T.4.

Note 6: The chromaticity coordinates x E , y E , z E of the equi-energy spectrum derived from the
sums Zx(A), Sy(A),Sz(l) of Table T.4 are

x E = 0,333 334

y E = 0,333 331 (6.2)

z E = 0,333 335

The small differences between the values of the chromaticity coordinates x E , y E , z E
are due to the limited number of decimal digits given in the table.

6.2 CIE 1964 standard colorimetric observer

For correlation with visual colour matching of fields of angular subtense greater than 4° at the
eye of the observer, it is recommended that colorimetric specifications of colour stimuli be

vm Table 1 of CIE standard colorimetric observers (CIE, 1986a) is reproduced in the CD-ROM
that accompanies this Technical Report.

10

CiE 15:2004

based on the colour-matching functions x 10 (A) ) yio(^). z io(^) published in the CIE Standard:
CIE standard coSorimetric observers (CIE, 1986a). A 10° visual field represents a diameter of
about 90 mm at a viewing distance of 0,5 m. These colour-matching functions are given in the
standard as values from 360 nm to 830 nm at 1 nm intervals with six significant figures, and
they define the CIE 1964 standard colorimetric observer (in technical applications often
written as 10°-standard colorimetric observer) lx in the case more coarsely sampled data will
produce no significant calculation error, the tables reproduced in Section 1 1 may be used
instead of the 1-nm interval data. The values given in Table T.5 at 5 nm intervals are selected
values from the standard, rounded to six decimal places.

Note 1: x 10 (A),y 10 (A),z 10 (>l) are the normalized tristimulus values of monochromatic

radiations for a set of reference stimuli [X 10 ], [Y 10 ], [Z 10 ] required to match each
wavelength of the equi-energy spectrum. Their levels are such that the maximum of
y w (A) is unity and 2x 10 (A) = 2y 10 U) = £z 10 (>l) (The equi-energy spectrum is
radiation whose spectral concentration of power as a function of wavelength is
constant.)

Note 2: The real reference stimuli [R 10 ], [G 10 ], [B 10 ] of the original trichromatic system are
related by transformation to the reference stimuli [X 10 ], [Y 10 ], [Z 10 ], which were
chosen for reasons of convenience in colorimetric computations (see Appendix B).
The colour-matching functions, x 10 (2), y 10 (A), z 10 (/t) are commonly used to obtain the
tristimulus values X 10 , Yio, Z 10 of colour stimuli.

Note 3: If the colour-matching functions of Table T.5 are required at closer intervals, the values
at 1 nm intervals given in the standard, CIE standard colorimetric observers (CIE,
1 986a) should be used. For values at other than the 1 nm intervals see Note 4 to 6. 1 .

Note 4: The chromaticity coordinates x 10 (A), y 10 (A), z 10 (^) of the spectral stimuli are the ratios

x 10 (A) = ^ ! 1o(A) _

x 10 (;i)+y 10 (/i) + z 10 (;,)

y 10 W=- I"™ _ (6.3)

XioW+yioW + ^oW

ZioW =

*io(>0

xioW+yioW+zioW

x 10 (A) and y 10 (A) are given in Table T.5.

Note 5: The chromaticity coordinates x 10 , E , yio,E» *io,e of the equi-energy spectrum derived
from the sums Ix 10 (2), Sy 10 (/L), Ez 10 (A) of Table T.5 are

X| 0> e = 0,333 298

y,o, E = 0,333 336 (6.4)

Zio.e = 0,333 366

The small differences between the values of the chromaticity coordinates x 10E , y 10 E,
z 10E are due to the limited number of decimal digits given in the table.

Note 6. The large-field colour matching data as defined by the CIE 1964 standard colorimetric
observer are intended to apply to matches where the luminance and the relative
spectral power distributions of the matched stimuli are such that no participation of
the rod receptors of the visual mechanism is to be expected. This condition of
observation is important as "rod intrusion" may upset the predictions of the standard
observer. For daylight, possible participation of rod vision in colour matches is likely
to diminish progressively above about 10 cd-rrf 2 and be entirely absent at about
200 cd-m" 2 . For further details see 12 .

iX Table 2 of CiE standard colorimetric observers (CIE, 1986a) is reproduced on the CD-ROM
that accompanies this Technical Report.

11

X = kZfa{A)xW)AA

X w = k w £^(A)x w (A)AA

A

Y = kj^(A)y(A)AA

Vio=*iof*iW)7ioW^

Z = kZ<j> k {X)z{A)AA

Z 10 =^ 10 2-^(A)z 10 (/t)zl/l

A

CIE 15:2004

The CIE 1931 and 1964 standard colorimetric observers were both derived from
trichromatic systems based on real red [Rj, green [G] and blue [B] primaries, see Appendix B.

7. RECOMMENDATIONS CONCERNING THE CALCULATION OF TRiSTIMULUS

VALUES AND CHROMATICITY COORDINATES 13

7.1 Calculation of tristimulus values

The CIE Standard (CIE, 1986a) on standard colorimetric observers recommends that the CIE
tristimulus values of a colour stimulus be obtained by multiplying at each wavelength the
value of the colour stimulus function <p x {A) by that of each of the CIE colour-matching
functions and integrating each set of products over the wavelength range corresponding to
the entire visible spectrum, 360 nm to 830 nm. The integration can be carried out by
numerical summation at wavelength intervals, AA, equal to 1 nm.

(7.1)

In the above equations <fi ? {A) denotes the spectral distribution of the colour stimulus
function, i.e. fa(A) = d^ytU, see CIE international Lighting Vocabulary item 845-01-17 (CIE,
1987). X, Y,Z are tristimulus values, x(A),y(A),z(A) are colour-matching functions of a
standard colorimetric observer, and k is a normalising constant defined below. Each of these
may be specified for the CIE 1931 standard colorimetric system by being written without a
subscript, or for the CIE 1964 standard colorimetric system by the use of the subscript 10.

The fundamental colorimetric tables are the 1 nm tables in CIE standards. All
rigorous calculations should use these 1 nm tables. For most practical purposes, the
summation may be approximated by using wavelength intervals, AX equal to 5 nm over the
wavelength range 380 nm to 780 nm. Values of the CIE colour-matching functions at 5 nm
intervals suitable for use in summation over this range of wavelengths are given in Tables T.4
and T.5. When measurements have been made at smaller intervals than 5 nm, the
appropriate values from the tables in the standards should be used.

Tristimulus values are usually evaluated on a relative basis. In such cases the
relative colour stimulus function, tp (A), may be used instead of the colour stimulus function,
fa{A) y but it is essential that, for stimuli that will be considered together, all the spectral
distributions involved be assessed on the same relative basis. The tristimulus values obtained
are then relative in the sense that all the values involved may be multiplied by the same single
arbitrary constant. In certain cases, however, k and /c 10 must be chosen according to agreed
conventions; these are explained in Sections 7.1.1 and 7.1.2.

Tristimulus values evaluated on a relative basis may need to be supplemented by the
value of a suitable absolute photometric quantity.

7.1.1 Secondary light sources (reflecting or transmitting objects)

For reflecting or transmitting object colours, the colour stimulus function, ^(A), is replaced by
the relative colour stimulus function, <j> {A), evaluated as

(HA) = R(A)-S{A) or <&A) = r{A)-S{A)

where; R(A) is the spectral reflectance factor (or spectral radiance factor or spectral
reflectance) of the object colour (preferably evaluated for one of the geometric
conditions given in Section 5.2).

t{A) is the spectral transmittance of the object colour (preferably evaluated for one
of the geometric conditions given in Section 5.3).

S(A) is the relative spectral power distribution of the illuminant (which, whenever
12

CI E 15:2004

possible, should be one of the CIE standard illuminants; see Section 3.1).
In this case, the constants, k and /c 10 , are chosen so that Y = 100 for objects for which
R(£), or r{A) = 1 for all wavelengths, and hence

k = 10Q/J^S{A)y(A)AA

(7.2)
* 10 =100/£S(A)y 10 U)A>l

A.

For other objects, the values of Y are then equal to the percentage values of
iuminous reflectance factor or luminance factor or luminous reflectance [in the case of R{A)],
or luminous transmittance or luminous transmittance factor [in the case of t(A)]\ this is
because the y(A) function is identical to the CIE spectral luminous efficiency function V(A)\

7.1.2 Illuminants and self-luminous objects

For self-luminous objects and illuminants, the constants, k and /c 10 , are usually chosen on the
grounds of convenience. If, however, in the CIE 1931 standard colorimetric system, the Y
value is required to be numerically equal to the absolute value of a photometric quantity, the
constant, k, must be put equal to the numerical value of K m , the maximum spectral luminous
efficacy (which is equal to 683 Im-W 1 ) and fa{A) must be the spectral concentration of the
radiometric quantity corresponding to the photometric quantity required.

7.2 The use of abridged or truncated data

The use of the tables published in the CiE standard on colorimetric observers (CIE, 1986a)
requires that the colour stimulus function, $ z (a), or the relative colour stimulus function, #(Z),
be known at 1 nm wavelength intervals over the wavelength range 360 nm to 830 nm. In
practical applications, all the required data may not be available because the measurement
was made at intervals greater than 1 nm, or unequal wavelength intervals were used, or data
at the spectral extremes were omitted (truncation). Often it is possible to predict the needed
but unmeasured data. It is recognised that calculation from predicted, rather than from
measured, data, or from abridged or truncated data, may be inexact, but the investigator can
often be satisfied that the accuracy is sufficient for the intended use of the tristimulus values.
It is important to use the same wavelength interval and range throughout for any set of
calculations in which data for different colours are to be compared precisely. In particular, it
should be noted that the exact values obtained for the perfect diffuser for a given illuminant
depend on the wavelength interval and range used 14 .

7.2.7 Abridgement

Abridgement of colour stimulus data by the use of a larger sampling interval, for example
10 nm or 20 nm, wiil lead to errors in the computed tristimulus values. Such abridgement
should be used only when it can be demonstrated that these errors are negligibly small for the
intended use of the tristimulus values. If these errors are not negligible, it is recommended
that needed but unmeasured values of <fi z (A) } R(A), or zfA) be predicted by adequate
interpolation.

Note 1: Spectral reflectance and transmittance curves are usually smooth enough and
continuous to permit interpolation, while e.g. spectral power distribution data of gas
discharge lamps are frequently not suited for interpolation. Using interpolated values
of spectral power distribution data of such lamps may lead to considerable errors.

x CIE Division 1 is currently investigating whether a V^ Q (A) function should be introduced,
where V W (A) ~ y 10 (A). interested parties should check the latest CIE publication list or the
recent edition of the International Lighting Vocabulary on the introduction of such a new
definition. At the closing of the present edition of CIE 15 no V^ q {a) function has been officially
agreed (for further details see Appendix B).

13

CIE 15:2004

Note 2: Measurement errors also arise from the bandwidth of a spectrometer. Even if the data
interval is 1 nm, the colorimetric errors can be significant if the bandwidth of the
spectrometer is large. See 7.2.5 for bandwidth requirements.

7.2.1.1 Interpolation

Use one of the four following methods to calculate needed but unmeasured values of fa(A),
R{a) or r(X) within the range of measurements: 1) the third-order polynomial interpolation
(Lagrange) from the four neighbouring data points around the point to be interpolated, or 2)
cubic spline interpolation formula, or 3) a fifth order polynomial interpolation formula from the
six neighboring data points around the point to be interpolated, or 4) a Sprague interpolation
(see Seve, 2003) XI

Note: Experiments have shown that for most samples showing smooth reflectance or
transmittance spectra, the computed tristimuius values will have an adequate
accuracy if measured data, illuminant and colour-matching function values at 5 nm
intervals are used. See also Note to Section 7.2.3.

7.2.2 Truncation

Where the measurement range is less than the practical range of summation, 380 nm to
780 nm, omission of values at the limits of the measurement range will lead to errors in the
computed tristimuius values. Such truncation should be used only when it can be demonstrated
that these errors are negligibly small for the intended use of the tristimuius values.

Note; If these errors due to limited measurement range are not negligibly small, the errors
might be reduced by adequate extrapolation of the needed but unmeasured values of
<j>iX), R(Z) or t(A). The range of the summation is an essentia! part of the tristimuius
specification.

7.2.2.1 Extrapolation

Extrapolation is generally not recommended. However, when predicting needed but
unmeasured values of ^(A) or <f{X) outside the range of measurements, in the absence of
other information, unmeasured values of fa(Z), [$(%)] or of p(A), /?(A), or r(X) may, as a rough
approximation, be set equal to the nearest measured value of the appropriate quantity in
truncation.

7.2.3 Weighting factors

In the case of repetitive calculations from measurements at the same wavelengths, it is often
convenient to perform only once those calculations that are independent of the measured
data. This results in a table of weighting factors. Such weighting factors should give results
consistent with those from the normal calculations. It is recommended that tables of weighting
factors be calculated for the full range of wavelengths, 360 nm to 830 nm. This provides
tables that may be used for any degree of truncation by adding the weights at the
unmeasured wavelengths to those at the extreme measured wavelengths. The sum of the
weights at the unmeasured wavelengths is a measure of the maximum error introduced by
truncation.

Note: If it has been checked that measurement data obtained only at 10 nm or 20 nm
intervals satisfy the need of the observer, computation methods as described e.g. in
ASTM (1999) might be used. This publication contains weighting factors for both the
CIE 1931 standard colorimetric observer and the CIE 1964 standard colorimetric
observer and a number of illuminants and practical light sources used in colorimetry.
Its Table 5 has been developed for the case when the instrument manufacturer has
built in a correction to zero bandwidth (see Fairman, 1985). Its Table 6 provides

XI

A CIE Technical Committee is currently working on a standardized method of interpolation,
interested parties should check the latest CIE publication list for more information. The CD-
ROM accompanying this report contains PC interpolation programs for linear, Lagrange,
spline and Sprague interpolation.

14

CIE 15:2004

weighting factors for the case when a correction to a zero bandwidth is required (see
also Venable, 1989; Li et al., 2004; ASTM, 2001 and ASTM, 2003).

7. 2. 4 Numerical procedures

It is recommended that all numerical calculations be carried out using the full number of
significant digits provided by the data in the Tables published in the CIE standards of
colorimetry. Final results should be rounded to the number of significant digits indicated by
the precision of the measurements.

Note 1 : For the purpose of calculating tristimulus values, the quantities involved for secondary
light sources shall be defined as points of a continuous distribution, each point
representing an infinitely narrow range of wavelengths. For primary light sources the
relative emitted power is regarded as emitted in a wavelength band equal to the
measuring interval and centred around the nominal wavelength.

Note 2: For colour stimulus functions of primary light sources that vary rapidly with
wavelength, the spectral bandwidth at half power of the measuring instrument used to
determine the colour stimulus function should be equal to, or an integer multiple of,
the measuring interval. For smoothly varying functions this restriction is less
important. For the highest accuracy, a bandwidth of 1 nm may be used for the
measuring instrument, but for most practical purposes a bandwidth and measurement
interval of 5nm may be used. The use of bandwidths of 10 nm, or 20 nm is not
recommended; it can lead to considerable loss of accuracy, and if applied, should be
checked on typical spectra. For practical measurements a trade-off between
bandwidth and signal-to-noise ratio has to be found, as the latter will influence
photometric accuracy. A signal-to-noise ratio of 1 : 1 0" 4 when measuring an ideal white
sample is adequate for most applications.

Note 3: The foregoing recommendations are based on measurements at equal intervals of
wavelength, it is, however, not intended to imply that summations may properly be
computed only with such intervals. Other summation procedures, including
specifically the method of selected ordinates, may be used providing that the
tristimulus values thus computed are consistent with those based on the above
recommendations.

7. 2. 5 Bandwidth of a spectrometer

When discussing errors associated with data intervals, it is also important to know
measurement errors (uncertainties) due to the bandwidth of a spectrometer because, in real
measurements, the data interval (scanning interval) and the bandwidth are closely related
with each other to affect the measurement results.

Measurement errors arising from the bandwidth of a spectrometer are generally much
larger (by an order of magnitude) than the calculation errors associated with data intervals.
Even if the data interval is 1 nm (or interpolated to 1 nm intervals), the colorimetric errors can
be significant if bandwidth of the spectrometer is large. See also Section 7.2.4 Note 2.

7.3 Calculation of chromaticity coordinates

It is recommended that chromaticity coordinates (x, y, z) be derived from the tristimulus
values (X, Y, Z) as follows;

X

X + Y + Z

y -x^kz (73)

z

z =-

X + Y + Z

Because of the relation x + y+z=1,it suffices to quote x, y only. The diagram using
the chromaticity coordinates x, y is referred to as the CIE 1931 chromaticity diagram or the
CIE (x, y) (chromaticity) diagram.

15

CIE 15:2004

Note: The chromaticity coordinates x 10 , yio, z w are computed simiiarly from the tristimulus
values X 10 , V10 , Z 10 ; the CIE 1964 chromaticity diagram is obtained using these
values.

7.4 Equations representing relationships between colour stimuli 16

When equations are used to represent relationships between colour stimuli, symbols of vector
notation should be used instead of those for numerical relationships. For example, one of the
following forms could be used:

[C].X[X]+Y[Y] + Z[Z]

or (7.4)

C = XX+YY+ZZ

where X } Y } Z are the tristimulus values of colour stimulus [C], or C. The unit vectors of the
reference stimuli are indicated either by [X], [Y], [Z], or by the boldface Roman letters X, Y, Z.
Note: In Equ. 7.4 the "= ' and "=" signs mean "matches".

8. RECOMMENDATIONS CONCERNING UNIFORM COLOUR SPACING AND

COLOUR DIFFERENCES 16

8.1 CIE 1976 uniform chromaticity scale diagram (UCS diagram)

The use of the following chromaticity diagram is recommended whenever a projective
transformation of the (x.yj-diagram yielding colour spacing perceptually more uniform than
that of the (x,y)-diagram is desired. The chromaticity diagram is produced by plotting

u' = 4X/(X+15Y+3Z)
as abscissa and (8.1)

v 1 =9YI(X+ 15Y+3Z)

as ordinate, in which X, V, 1 are tristimulus values. The third chromaticity coordinate w' is
equal to (1 - u' - v 1 ).

Note 1: The colour spacing afforded by this chromaticity diagram is known to be perceptually
more uniform than that of the CIE (x f y)-chromaticity diagram for observation of
samples having negligibly different luminances (e.g. for AY<0,5). This diagram is
intended to apply to comparisons of differences between object colours of the same
size and shape, viewed in identical white to middle-grey surroundings, by an observer
photopically adapted to a field of chromaticity not too different from that of average
daylight.

Note 2: The same chromaticity diagram is produced by plotting

u'= 4x / (-2x + 1 2y + 3) as abscissa and

v' = 9y / (-2x + 1 2y + 3) as ordinate, (82)

where x, y are chromaticity coordinates.

Note 3: If the angle subtended at the eye by the pairs of specimens being compared is more
than 1° and less than about 4°, the tristimulus values X, Y, Z (or chromaticity
coordinates x, y), calculated using the CIE 1931 standard colorimetric observer
should be used for the calculation of u' and v'. If the angle is greater than 4°, the
tristimulus values X 10 , Y 10 , Z 10 , (or chromaticity coordinates x 10 , yio) of the CIE 1964
standard colorimetric observer should be used to calculate u\ and v' 10 .

Note 4: The CIE 1960 UCS diagram, now obsolete, is described briefly in Appendix A.3.

8.2 CIE 1976 uniform colour spaces

Pending the development of an improved coordinate system 17 , the use of one of the following
coordinate systems is recommended whenever a three-dimensional spacing perceptually
more nearly uniform than that provided by the XYZ system is desired.

16

CIE 15:2004

8.2.1 CIE 1976 (L*a*b*) colour space; CIELAB colour space

8.2.1.1 Basic coordinates

Three-dimensional, approximately uniform, colour space produced by plotting in rectangular
coordinates, L* a* b*> quantities defined by the equations

Z_* = 116f(WY n )-16

(8-3)

a* = soo[/(x/Xn)-/(y/y„)]

(8.4)

b* = 2QQ[f{YIY n )-f{ZIZ n )]

(8.5)

f(X/X n ) = (X/X n ) 1/3

if

(X/X n )>(24/116) 3

(8.6)

f(X/X n ) = (841/108)(X/X n )+16/116

if

(X/X n )<(24/116) 3

(8.7)

f(y/y n )-(wy n ) 1/3

if

(y/y n )> (24/1 16) 3

(8.8)

f{Y/Y n ) = (841/108)(Y/y n ) +16/116

if

(y/y n )< (24/1 16) 3

(8.9)

f(Z/Z n ) = (Z/Z n ) 1/3

if

(Z/Z n )> (24/1 16) 3

(8.10)

/(Z/Z n ) = (841/108)(Z7Z n ) +16/116

if

(Z/Z n )< (24/1 16) 3

(8.11)

where

and

and

where X,Y,Z are the tristimulus values of the test object colour stimulus considered and X n ,
y n; Z n are the tristimulus values of a specified white object colour stimulus. In most cases, the
specified white object colour stimulus should be light reflected from a perfect reflecting
diffuser illuminated by the same light source as the test object. In this case, X n , Y n , Z n are the
tristimulus values of the light source with Y n equal to 100 18 \

The informative annex Appendix D describes the recommended reverse
transformation of the L*, a*, b* coordinates to X, Y, Z tristimulus values.

8.2.1.2 Correlates of lightness, chroma and hue

Approximate correlates of the perceived attributes lightness, chroma and hue are calculated
as follows

CIE 1976 lightness: L* as defined in Equ. 8.3.

CIE 1976 a,b (CIELAB) chroma : C* ab = (a* 2 + 5* 2 ) 1/2 (8.12)

CIE 1976 a ; b (CIELAB) hue angle: h ab = arctan (bVa*) (8.13)

see Section 8.2.3 Note 1 and Note 2.

8.2.1.3 Colour differences

Euclidean distances in CIELAB colour space can be used to represent approximately the
perceived magnitude of colour differences between object colour stimuli of the same size and
shape, viewed in identical white to middle-grey surroundings, by an observer photopically
adapted to a field of chromaticity not too different from that of average daylight. In cases of
deviating conditions the correlation between calculated and perceived colour differences may
be impaired.

Differences between two samples (denoted by subscripts and 1) shall be calculated
as follows:

CIELAB lightness difference: A/_* = L\ - L\ (8.14)

Aa* = a* 1 -a* (8.15)

Ab* = b\ - b* (8.16)

CIELAB chroma difference: AC* ab = C* ab ,i - c Vo (8.17)

17

CIE 15:2004

CIELAB hue angle difference: A/? ab = h abtl - h abi p (8.18)

If the line joining the two colours crosses the positive a* axis, Equ. 8.18 will give a value
outside the range ±180°, in this case, the value of Ah ab must be corrected by adding or
subtracting 360° to bring it within this range, see also Section 8.2.3 Note 4.

CIELAB hue difference AH* ab = 2(C* abir C* abj0 ) 1/2 -sin(A/? ata /2) (8.19)

for small colour differences away from the achromatic axis

AH% b = (C* ab( rCVo) 1/2 -A^ ab (8.20)

where the value of A/? ab is in radians.

Note 1: The calculation of CIELAB hue and chroma differences is progressively less useful as
the absolute value of Ah ab approaches 1 80°.

Note 2: In information technology and other fields the subscript (R) is sometimes used for
reference and (T) for test instead of (0) and (1). Similarly in industrial evaluation of
small colour differences (s) is sometimes used for standard and (b) for batch.

CIE 1976 a,b (CIELAB) colour difference, AE* ab between two colour stimuli is calculated as
the Euclidean distance between the points representing them in the space:

AE* ab =lAL*Y+{Aa*Y+(*b*f]' 2

(8.21)

or

AE

ab

M"

+ |AC* ab | +\AH"

(8.22)

these two definitions of AE* ab are equivalent.

Alternative ways of calculating AH* ab are:

AH

ab ■

(AE*J-(M*y-(*C*Jj

where AE* ab is calculated from Equ. 8.21 , and AH* ab has the same sign as A/? ab ;

-|1/2

AH% b =/f2JCVi-C* ab ,o-aVa*o-bVfcV

(8.23)

(8.24)

where k = -1 if a *, • b * > a * • b * 1 , otherwise k = 1 ;

and

AH* ab = \a\-b%-a\-b\ I

0,5C* aby C% bfl+ a%-a\+b%-b*

1/2

(8.25)

More details on these alternative methods of calculating A/-/* ab are given in Seve
(1991), Stokes and Brill (1992) and Seve (1996).

Note: In different practical applications it may be necessary to use different weightings for
AL*, AC* ab) and A/-/* ab . In 2001, the CIE recommended such weightings in a new
formula for industrial evaluation of small colour differences (CIE, 2001a), see Section
8.3.

8.2.2 CIE 1976 (L*u*v*) colour space; CIELUV colour space

Three-dimensional, approximately uniform, colour space produced by plotting in rectangular
coordinates, L* u*, v*, quantities defined by the equations

L* = 116 f(YIY n )- 16
See also Equ. 8.3, where

nyiYn) = (YiY n )

if (WV n ) >

24
TT6

(8.26)
(8.27)

18

CI E 15:2004

f(Y/Y n ) = (841/108)(Y/Y n ) +16/116 if (V/V n ) < I — 1 (8.28)

J16J

and

u* = 13L*(u'-u'n) (8.29)

v* = 13L*(v' - v' n ) (8.30)

where Y, u', v' describe the colour stimulus considered and Y n , u' n , v' n describe a specified
white object colour stimulus.

Approximate correlates of lightness, saturation, chroma, and hue may be calculated
as follows:

CIE 1976 lightness: L* as defined in Section 8.2.1.1

and Equ. 8.26.
CIE 1976 u } v (CIELUV) saturation: s u , v = 1 3 [(u' - u' n ) 2 + {vW n f] m (8.31)

CIE 1976 u,v (C1ELUV) chroma: C* uv = (u* 2 + v* 2 ) 1 ' 2 = L*s w (8.32)

CIE 1976, u.y (CIELUV) hue-angle: h m = arctan[(v' - v' n )!(u' - u\)\

= arctan(v*/u*) (8.33)

See 8.2.3, Note 2.

CIE 1976 u, v (CIELUV) hue-difference: AH* UV = 2(C Vi • C * uv ,o) 1/2 sin(A/) uv /2) (8.34)

where 1 and refer to the two samples between which the colour difference is to be
calculated and A/7 UV = h uvA - /? UVi0 (see Seve ,1991).

CIELUV colour difference A£* uv between two colour stimuli is calculated as the Euclidean
distance between the points representing them in the space:

AE* UV = [(AL*) 2 + (Au*f + (Av*) 2 ] 1/2 (8.35)

For an alternative ways to calculate AH* UV , see the description in 8.2.1 , but change a*
to u* and b* to v*.

8.2.3 Notes on CIE 1976 uniform colour spaces

Note 1: When the linear formulae (Equ.'s 8.7, 8.9 or 8.11) are used for X/X n , Y/Y n ox ZIZ n ,
anomalous values of h ab may be obtained (McLaren, 1980). Anomalous values are
unlikely to occur for surface colours but may occur for transparent object colours of
low luminance factor lying close to the spectrum locus or purple line.

Note 2: h ab (or h uv ) lies between 0° and 90° if a* and b* (or u* and v*) are both positive,
between 90° and 180° if b* (v*) is positive and a* (u*) is negative, between 180° and
270° if b* and a* (v* and u*) are both negative, and between 270° and 360° if b* (v*)
is negative and a* (u*) is positive.

Note 3: CIE 1976 a,b and u,v hue-differences are introduced so that a colour difference AE*
can be broken up into components AL*, AC* : and AH* whose squares sum to the
square of AE*. Differences in CIE 1976 a,b or u,v hue-angle, &h ab (or A/? uv ), do not
have this property.

Note 4: If the line joining the two colours crosses the positive a* (or u*) axis, the value of A/7 ab
(or Ah uv ) must be corrected by adding or subtracting 360° to bring it into the range
±180°.

Note 5: These spaces are intended to apply to comparisons of differences between object
colours of the same size and shape, viewed in identical white to middle-grey
surroundings, by an observer photopically adapted to a field of chromaticity not too
different from that of average daylight.

Note 6: If the angle subtended at the eye by the pairs of object colours being compared is
between about 1° and 4° the tristimulus values X, Y, Z calculated with respect to the
CIE 1931 standard colorimetric observer should be used for the calculation of L* a*
/>*, u* v* and hence AE* ab , C* ab , s uv , C* uv , h ab , h uv , AH* ab , AH* UV . If the angle is greater

19

CIE 15:2004

than 4°, the tristimulus values X 10 , V 10l Z 10 calculated with respect to the CIE 1964
standard colorimetric observer should be used to calculate L* 10 , a* 10 , *>*io. u* 10 , v*io,
and hence AE* a b,ioi C* a b,ioi s uv,ioj C* UVi io. ^at>,io, ^Wioi ^^*ab,io. AH* UVj io-

Note 7: The obsolete CIE 1964 uniform colour space and colour difference formula are
described briefly in the Appendix A.

Note 8: In different practical applications it may be necessary to use different weightings for
AL*, AC*, and AH*, see Section 8.3.

Note 9: Equ.'s 8.21 to 8.25 and 8.35 have been replaced for small colour differences by the
new recommendation of the CIE, see Section 8.3.

8.3 Improved industrial colour difference evaluation

8.3. 1 CIEDE2000 total colour difference formula

The CIE 1976 uniform colour spaces provide for the calculation of colour differences as
vector distances in those spaces, industrial practice with small colour differences has shown
non-uniform effects with calculated values in different ranges and different directions in those
spaces. Moreover, a change of external observing conditions may change the perceived
magnitude of the colour difference in a sample pair. The work documented in CiE 101-1993
(CIE, 1993) describes a number of external parameters of a visual task that affect the
correlation of visual magnitude judgements of colour differences with their colorimetric
measures. The outcome of those studies was the definition of reference conditions of a visual
task to which a colour-difference formula should be adapted. Experimental data sets must
now be chosen to meet reference conditions or to clearly define quantified deviations from
them.

The CIEDE2000 total colour difference formula corrects for the non-uniformity of the
CIELAB colour space for small colour differences under reference conditions. Improvements
to the calculation of total colour difference for industrial colour difference evaluation are made
through corrections for the effects of lightness dependence, chroma dependence, hue
dependence and hue-chroma interaction on perceived colour difference. The scaling along
the a* axis is modified to correct for a non-uniformity observed with grey colours. The
resulting recommendation is as follows (CIE, 2001a) Xh :

^00 =

AL'
k L S L

AC

AH'

+ R T

( AC

AH'

&

(8.36)

A localized modification of the scaling along the a* (red-green opponent) axis is made
to improve agreement with visual colour-difference perception for neutral colours. The
modification increases the magnitudes of a' values compared to a* values for colours at low
chroma. The transformation is as follows:

L'=L*

a'^a*{UG)

b'=b*

(8.37)

G=0,5

1 i

*7
ab

c

+25 7

(8.38)

The transformed L', a', b' values are used in calculation of hue angle, chroma and
lightness, chroma and hue differences and these quantities are designated by a prime mark
in the equations.

Xil We follow here the terminology used in CIE 142-2001 (CIE, 2001a), and omit the subscript
"10", although C1EDE2000 is recommended for sample size larger than 4 degrees and thus

the 10 degree observer has to be used.

20

CIE 15:2004

Weighting functions, S L , S c , S H adjust the total colour-difference for variation in
perceived magnitude with variation in the location of the colour-difference pair in L' a', b'
coordinates.

Sl=1+ 0/015 (/?~50f (8.39)

V20 + (l'-50]P

S C =1 + 0,Q45C' (8.40)

S H =1 + 0,015CT (8.41)

T -1-0,17 cos(/?-3o) +0,24 cos(2h')+0,32 cos(3rt'+6)-0,20 cos(4/t"'-63) (8.42)

Visual colour-difference perception data show an interaction between chroma
difference and hue difference in the blue region that is observed as a tilt of the major axis of a
colour-difference ellipsoid from the direction of constant hue angle. To account for this effect,
a rotation function is applied to weighted hue and chroma differences.

R r = -$\n(2AG)R c (8.43)

A0 - 30exp {- [(/?-275)/25J 2 } (8.44)

R C -2J^ 7 C ' 7 _ (8.45)

Mean hue angle and A6> values are in degree units.

Note 1 : All quantities with a super-position bar indicate the mean of the values for each of the
samples of a colour-difference pair.

Note 2: The parametric factors, k L , /c c , k H are correction terms for variation in experimental
conditions. Under reference conditions they are all set at 1 . For other choices see
(CIE, 1993). The reference conditions are:

Illumination: source simulating the spectral relative irradiance of CIE

standard iiluminant D65.

Illuminance: 1000 Ix.

Observer: normal colour vision.

Background field: uniform, neutral grey with /_* = 50.

Viewing mode: object.

Sample size: greater than 4 degrees subtended visual angle.

Sample separation: minimum sample separation achieved by placing the sample

pair in direct edge contact.
Sample colour-
difference magnitude: to 5 CIELAB units.

Sample structure: homogeneous colour without visually apparent pattern or non-
uniformity.

Note 3: An alternative colour difference formula (CMC formula) not developed by the CIE, but
used by some ISO committees, is briefly described in Appendix A.5 for reference
purposes.

Note 4: A further colour difference formula based on a modified colour space derived from
CIELAB is the DIN 99 formula (DIN, 2003), see Appendix A 6.

21

CIE 15:2004

9 RECOMMENDATIONS CONCERNING MISCELLANEOUS COLORIMETRIC

PRACTICES AND FORMULAE

9.1 Dominant wavelength and purity 19

When it is desired to express chromaticity in terms of dominant (or complementary)
wavelength and purity, it is recommended that the evaluations be carried out as follows.

9.1.1 Dominant wavelength (of a colour stimulus), A^

Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions
with the specified achromatic stimulus, matches the colour stimulus considered.

Note: For stimuli whose chromaticities lie between those of the specified achromatic
stimulus and the two ends of the spectrum, complementary wavelength is used
instead of dominant wavelength.

9.1.2 Complementary wavelength (of a colour stimulus), ^

Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions
with the colour stimulus considered, matches the specified achromatic stimulus.

Note: See note to dominant wavelength.

9.1.3 Colon metric purity, p c
Quantity, p c , defined by the relation

p c = L d /(L d + L n ) (9.1)

where L d and L n are, respectively, the luminances of the monochromatic stimulus and of the
specified achromatic stimulus that match the colour stimulus considered in an additive
mixture.

Note 1: In the case of stimuli characterized by complementary wavelength, suitable mixtures
of light from the two ends of the spectrum are used instead of the monochromatic
stimulus, and colorimetric purity should then be calculated using the equation given in
Note 2.

Note 2; in the CiE 1931 standard colorimetric system, colorimetric purity is related to
excitation purity (see 9.1.4), p e , by the equation

Pc = PeYd // (9.2)

where y d and y are the y-chromaticity coordinates, respectively, of the monochromatic
stimulus and the colour stimulus considered.

Note 3: In the CIE 1964 standard colorimetric system, the colorimetric purity, p c , 10 is defined
by the relation given in Note 2, but using p eil0 , ycuo, and y 10 instead of p e , y d , and y

9. 1.4 Excitation purity p e

Quantity, p e , defined by the ratio NCIND of two collinear distances on the chromaticity
diagram of the CIE 1931 or 1964 standard colorimetric system, the first distance being that
between the point C representing the colour stimulus considered and the point N representing
the specified achromatic stimulus; the second distance being that between the point N and
the point D on the spectrum locus at the dominant wavelength of the colour stimulus
considered. The definition leads to the following expressions:

p IzLl. or p e =±zln- (9.3)

Yd-Vn ><d-Xn

where (x, y), (x n , y n ), (x d , y d ) are the x, y chromaticity coordinates of the points C, N and D,
respectively.

Note 1: For colour stimuli for which no dominant wavelength exists, see Note 1 under
colorimetric purity (Section 9.1.3).

22

CI E 15:2004

Note 2: The formulae in x and y are equivalent but the use of that which has the greater value
in the numerator results in greater precision.

Note 3: Excitation purity is related to colorimetric purity by the equation:

Pe = Pc ylVt, Or Pe.10 = Pc.10 VvJYw

9.2 Special metamerism indices 20

Two specimens having identical tristimulus values for a given reference illuminant and
reference observer are metameric if their spectral radiance distributions differ within the
visible spectrum. The procedures concerned with a special metamerism index for a change
from a reference illuminant to a test illuminant of different spectral composition, or that for a
change from a reference observer to a test observer of different colour-matching functions are
called the determination of special metamerism indices.

A measure of the metamerism for the two specimens is the colour difference between
the two metameric specimens caused by substituting an illuminant, "special metamerism
index: change in illuminant", and caused by substituting an observer, "special metamerism
index: change in observer". The colour difference is evaluated using a CIE colour difference
formula and it must be clearly stated which formula has been used.

It is recommended that for two specimens whose corresponding tristimulus values
(Xi - X 2 , Yi = Y 2 , Zi = Z 2 ) are identical with respect to a reference illuminant and observer,
the metamerism index, M, be set equal to the colour difference A£* ab between the two
specimens computed for the test illuminant or for the test observer.

9.2. 1 Special metamerism index: change in iliuminant

This procedure defines a special metamerism index M itm for a change from a reference
illuminant to a test illuminant of different spectral composition.

Note: The metamerism index M j!m is not suitable for determining the resultant colour shift or
specifying the colour constancy of a single object colour when the illuminant is
changed.

9.2.1 .1 Tristimulus values under reference illuminant

For a pair of metameric object colours, their tristimulus values X rh Y Ti} Z r/ (/" = 1, 2) under a
reference illuminant are computed by the usual CIE recommendation (see Section 7) as

(9.4)

for m-r (reference illuminant), where p t (X) is the spectral reflectance of the metameric pair
( / = 1 , 2), S(a) is the spectral power distribution of the reference illuminant, and x(Z) , y{X) ,

z{a) are the colour-matching functions of either the CIE 1931 or 1964 standard colorimetric
observers. It should be stated which observer has been used, and

100

(9.5)

X m ,i

X

P A) S(X)

x(X) AX

' m,i

A

p{X) S(X) y(X) AX

^■m,i '

=*z

PkX) S(^)

z(X) AX

X

The preferred reference illuminant is CIE standard illuminant D65. If another
illuminant is used as reference, this should be noted.

For the set of the tristimulus values X Tih Y Xth Z rJ (/ = 1 ,2), the following relation holds by
definition.

x r .i=x ri2l r r ,i-y r , 2 , z n1 =z rT2 (9.6)

23

CIE 15:2004

If Equ. 9.6 fails to hold exactly, a suitable account should be taken of this failure. The
nature of such account should be completely specified and the size of the failure recorded.
See Note 1 after 9.2.2.3.

9.2.1 .2 Tristimulus values under test iliuminant

For the same pair of metameric object colours, their tristimulus values X u , y M ,Z t) ,- (/ = 1, 2)
under test iliuminant are computed from Equ. 9.4 with m~{, by inserting the spectral power
distribution of the test iliuminant into S(X).

Suitable test illuminants include CIE standard iliuminant A and the FL- and HP-
illuminants defined in Table T.6 and T.7.

The FL-illuminants represent typical fluorescent lamps 21 . Colorimetric data for these
illuminants 3re given in Table T.8. For the colour rendering index calculation the method as
described in CIE 13.3 (CIE, 1995b) was used. The most appropriate choice of test iliuminant
depends upon application, but where only a few typical FL-i!luminants are to be selected,
FL2, FL7 and FL1 1 should take priority.

The HP-illuminants are typical high-pressure lamp spectra used at the time of
publishing this report 22 . It may be useful to determine the metamerism index with respect to
several test illuminants. The specific test iliuminant used must be identified as a subscript to
M, e.g. M Aiiim orM FL11rilmi etc.

9.2.1 .3 Colour difference and metamerism index

The colour difference A£* ab is computed between the tristimulus values X t>1 , / u , Z u of object
colour 1 , and X t2 , Yt, 2 > A,2 of object colour 2. Then the metamerism index M ilm is defined as

M„ m = A£* ab (9.7)

If colour difference formulas other than CIELAB are used, this should be noted.

9.2.2 Special metamerism index; change in observer

The CIE 1931 and 1964 standard colorimetric observers represent the colour vision
properties of the average population reasonably well. Nevertheless it is well known that
individual deviations in the colour-matching functions occur among colour normal observers.

The special metamerism index: change in observer (CIE, 1989) was introduced to
describe the average degree of mismatch found among metameric colours if the colour-
matching functions of one of the standard colorimetric observers are changed to those of a
standard deviate observer of normal colour vision.

9.2.2.1 Tristimulus values for standard colorimetric observers

For a pair of metameric object colours, their tristimulus values X Uh Y ,Z tJ (i ~ 1, 2) for the
standard colorimetric (reference) observers are computed from Equ. 9.4, with n7=r, by use of
either the CIE 1 931 or 1 964 colour-matching functions.

If the two metameric object colours fail to be a precise match with respect to the
standard colorimetric observer, a suitable account should be taken of this failure. The nature
of such account should be completely specified and the size of the failure recorded. See Note
1 after 9.2.2.3.

9.2.2.2 Tristimulus values for standard deviate observer

For the same pair of metameric object colours, their tristimulus values X u , Y t;h Z tJ (i - 1 , 2) for
the standard deviate (test) observer are computed from Equ. 9.4, with rn=t, by inserting the
colour-matching functions x 6 {A), y 6 {A), z d (i) of the standard deviate observer. The colour-
matching functions x d (A), y d (/L), z d (2)are given by

24

CIE 15:2004
x d (A)= x(A) + Ax(2)

y d W= yW + Ayw (9.8)

z d (A)= z(A) + AzU)

where Ax(^) , Ay (A) , Az(A) are the so-called first deviation functions defined in Table 1.1 of
(CIE, 1989) and are reproduced in Table T.10.

9.2.2.3 Colour difference and metamerism index

The colour difference AE* ab is computed between the tristimulus values X t> i, Y t ,i> Zt,i of object
colour 1 , and X ti2 , Y ti2l Z ti2 of object colour 2. Then the metamerism index M obs is defined as

M ob5 = AE* ab (9.9)

If a colour difference formula other than CIELAB is used, this should be included in
the parenthesis as e.g. M obs (u*v*).

Notes on special metamerism indices

Note 1 : When the samples are not exactly metameric, that is X r1 ^ X r>2 , Y r>1 ^ Y r;2)
Z r1 ^Z r2 , then the tristimulus values X t2 , Y t2 , Z t2 are adjusted by the multiplicative
method as follows.

X\,2 ~ ^t,2 (Ka I X r2 ), Y' t ,2 = Y t)2 ( Yr.1 ' Y ri2 ), Z' t 2 = Z t ,2 (^r,1 ' ^2) (9.1 0)

Note 2: Each colour normal observer shows a colour difference AE*, for a sample pair
metameric with respect to a reference observer and an irradiating illuminant. About
95 % of APs for colour normal observers are usually found to be within 2 AM obs (a*b*
or u*v*).

Note 3: Further characterization of the observer metamerism can be done by calculating the
range of colour mismatch, see (CIE, 1989).

9.3 Assessment of the quality of a daylight simulator for coiorimetry 23

The quality of simulators of CIE daylight illuminants D50, D55, D65 and D75 can be assessed
by calculating the special metamerism index for change in illuminant, employing specified
samples that are metameric matches for the CIE illuminants D50, D55, D65 and D75,
respectively, and the CIE 1964 standard colorimetric observer. The purpose of this
assessment is to quantify the suitability of a test source as a practical reproduction of CIE
standard illuminant D50, D55, D65, or D75for colorimetric tasks 24 .

The basis for the assessment is the special metamerism index: change in illuminant
(see Section 9.2.1), employing specified samples that are metameric matches for the
standard daylight illuminant and the CIE 1964 standard colorimetric observer. The method
quantifies the mismatch resulting when samples that are a match under the standard daylight
illuminant are viewed under the illumination of the test source, the CIE 1964 standard
colorimetric observer being used throughout.

A visible range metamerism index is employed to evaluate the colorimetric suitability
of the test source for the visible wavelength range. Tables of spectral reflection radiance
factor define the metameric samples.

An ultraviolet range metamerism index is employed with a second set of metameric
samples to evaluate the suitability of the test source in relation to ultraviolet-excited
luminescent colours. The metameric sample pairs for this assessment are comprised of a
luminescent and a non-luminescent sample, which are spectrally identical matches for the
standard daylight illuminant. The non-luminescent sample in each metameric pair is specified
by values of spectral reflection radiance factor for each standard daylight illuminant (D50,
D55, D65, and D75).

25

CIE 15:2004

The luminescent sample in each metameric pair is specified by values of spectral
reflection radiance factor, relative spectral distribution of radiance emitted by fluorescence,
and spectral external radiant efficiency.

The ultraviolet range metamerism index quantifies the failure of the spectrally
identical match between the luminescent and the non-luminescent sample pairs resulting
from changing the illuminating source from a standard daylight illuminant to a test source.

Detailed description of the test method, including the tables needed for calculating
the quality index, and a computer program of the calculation method on disk, are published in
CIE 51.2-1999 (CIE, 1999c), see also (CIE, 2001b).

9.4 The evaluation of whiteness 25

To promote uniformity of practice in the evaluation of whiteness of surface colours, it is
recommended that the formulae for whiteness, IV or W 10j and for tint, T w or 7" W|10 , given below,
be used for comparisons of the whiteness of samples evaluated for CIE standard illuminant
D65. The application of the formulae is restricted to samples that are called "white"
commercially, that do not differ much in colour and fluorescence, and that are measured on
the same instrument at nearly the same time. Within these restrictions, the formulae provide
relative, but not absolute, evaluations of whiteness, that are adequate for commercial use,
when employing measuring instruments having suitable modern and commercially available
facilities.

W = Y + 800(x n - x) + 1 700(y n - y)

W10 = Vio + 800(x ni10 -x 10 ) + 1700(y ni1 o-yio) (9.11)

Tw = 1000(x n -x)-650(y n -y)

7"w,io = 900(x n , 10 ~x 10 )-650(y n , 10 -yio)

where Y is the V-tristimulus value of the sample, x and y are the x, y chromaticity coordinates
of the sample, and x n , y n are the chromaticity coordinates of the perfect diffuser, all for the
CIE 1931 standard colorimetric observer; Y 10l x 10 , yio, x n ,io and y ni10 are similar values for the
CIE 1964 standard colorimetric observer.

Note 1: The higher the value of Wot i/V 10 , the greater is the indicated whiteness. The more
positive the value of T w or 7 w10j the greener the tint; the more negative the value of T w
or T w10 , the redder the tint. For the perfect diffuser W and LV 10 are equal to 100, and
T w and T W)10 are equal to zero.

Note 2: Linear whiteness formulae are applicable only within a restricted volume of the colour
solid. These formulae may be used only for samples whose values of W or 1/V 10 and
T w or T w>10 lie within the following limits:

Wot W 1Q greater than 40 and less than 5Y- 280, or 5Y 10 - 280;

7" w or 7" W|10 greater than -4 and less than +2.

Note 3: The tint formulae are based on the empirical results that lines of equal tint run
approximately parallel to lines of dominant wavelength 466 nm in the x, y and x 10 , yio
chromaticity diagrams.

Note 4: Equal differences in Wot W w do not always represent equal perceptual differences in
whiteness, nor do equal differences in 7 W or T w10 always represent equal perceptual
differences in greenishness or reddishness of whites. Measures of whiteness and tint
that correlate uniformly with these perceptual attributes would require more
complicated formulae, which is beyond present knowledge.

9.5 Calculation of correlated colour temperature 26

The concept of correlated colour temperature used to be based on visual observations.
Recent investigations have shown (see Borbely et al., 2001) that no metrological definition
can be based on such perceptual investigations. Therefore a new definition has been
proposed. The definition agrees with the previously recommended calculation method and
thus does not cause any changes to calculated values.

26

CiE 15:2004

correlated colour temperature (7 cp )

temperature of a Pianckian radiator having the chromaticity nearest the chromaticity
associated with the given spectral distribution on a diagram where the (CIE 1931 standard
observer based) u\ 2/3v' coordinates of the Pianckian locus xm and the test stimulus are
depicted

Note 1 : The concept of correlated colour temperature should not be used if the chromaticity of

the test source differs more than AC = [(u\-u' P ) 2 + i.*(v' t -v' P ) 2 ] 1/2 = 5-10" 2 from the

9

Pianckian radiator, where u\,v\ refer to the test source, u' P y P to the Pianckian

radiator.

Note 2: Correlated colour temperature can be calculated by a simple minimum search
computer program that searches for that Pianckian temperature that provides the
smallest chromaticity difference between the test chromaticity and the Pianckian
locus, or e.g. by a method recommended by Robertson (1968).

10. REFERENCES

ALMAN, D.H., BSLLMEYER, F.W. JR., 1976. Integrating sphere errors in the colorimetry of
fluorescent materials. Color Res. Appl., 1, 141-145, 1976.

ASTM, 1999. American Society for Testing and Materials Standard E 308. Standard practice
for computing the colors of objects by using the CiE system, 1999.

ASTM, 2001. American Society for Testing and Materials E-2022-01. Standard practice for
calculation of weighting factors for tristimulus integration, 2001 .

ASTM, 2003. American Society for Testing and Materials Standard E2022-01. Standard
practice for calculating of weighting factors for tristimulus integration, 2003. see e.g. ASTM
Book of Standards Vol. 06.01

BORBELY, A., SAMSON, A., SCHANDA, J., 2001. The concept of correlated colour
temperature revisited. Color Res. Appl., 28/6, 450-457, 2001.

CIE, 1931. Proc. of the 8th Session of CIE, Cambridge, 19-29, 1931.

CIE, 1948. Proc. of the 11th Session of CIE, Paris, 16, 1948.

CIE, 1951. Proc. of the 12th Session of CiE, Stockholm, Vol. 3, 63, 1951.

CIE, 1955. Proc. of the 13th Session of CIE, Zurich, Vol. 1, Section 1.3.1, 12-13, 1955.

CIE, 1957. CIE Bulletin No. 3, 16, 1957.

CIE, 1959. Proc. of the 14th Session of CIE, Brussels, Vol. A, 91-109, 1959.

CIE, 1963. Proc. of the 15th Session of CIE, Vienna, Vol. A, 35, 1963.

CIE, 1967. Proc. of the 16th Session of CiE, Washington, D.C., Vol. A, 95-97, 1967.

CIE, 1971. CIE 15-1971. Colorimetry, 1971.

CIE, 1972. Supplement No. 1 to CIE 15-1971 Special metamerism index: Change in
illuminant, 1972.

CIE, 1978. Supplement No. 2 to CIE 15-1971. Recommendations on uniform colour spaces,
colour-difference equations, psychometric colour terms, 1978.

CIE, 1979a. CIE 44-1979. Absolute methods for reflection measurements, 1979.

CiE, 1979b. CIE 46-1979. A review of publications on properties and reflection values of
material reflection standards, 1979.

XIM In calculating the chromaticity coordinates of the Pianckian radiator the c 2 value according
to ITC-90 has to be used (c 2 = 1 ,4388) in Planck's equation for standard air, but assuming
n=1. See Appendix E.

27

CIE 15:2004

CIE, 1981. CIE 51-1981. A method for assessing the quality of daylight simulators for
coiorimetry, 1981.

CIE, 1986a. CiE S002-1986. CIE standard colorimetric observers, 1986. (Published also as
C IE/ISO 10527:1991).

CIE, 1986b. CIE 15.2-1986. Coiorimetry, Second Edition, 1986.

CIE, 1987. CIE 17.4-1987. International Lighting Vocabulary, 1987.

CIE, 1988. CIE 76-1988. Intercomparison on measurement of (total) spectral radiance factor
of luminescent specimens, 1988.

CIE, 1989. CIE 80-1989. Special metamerism index: Change in observer, 1989.

CIE, 1993. CIE 101-1993. Parametric effects in colour difference evaluation, 1993.

CIE, 1995a. CIE 116-1995. Industrial colour difference evaluation, 1995.

CIE, 1995b. CIE 13.3-1995. Method of measuring and specifying colour rendering properties
of light sources, 1995.

CIE, 1998a. CiE 131-1998. The CIE 1997 interim colour appearance model (simple version),
CIECAM97S, 1998.

CIE, 1998b. CIE x014-1998. Proc. of the CiE expert symposium '97 on colour standards for
imaging technology, 1998.

CIE, 1998c. Standard CiE S005/E-1998. CIE standard illuminants for coiorimetry, 1998.
(Published also as ISO 10526/CIE S 005/E-1999).

CIE, 1998d. CIE 130-1998. Practical methods for the measurement of reflectance and
transmittance, 1998.

CIE, 1999a. CiE 135/4-1999. Some recent developments in colour difference evaluation,
1999.

CiE, 1999b. CIE 135/3-1999. Supplement 1-1999 to CIE 51-1981, Virtual metamers for
assessing the quality of simulators of CIE illuminant D50, 1999.

CIE, 1999c. CIE 51.2-1999. A method for assessing the quality of daylight simulators for
coiorimetry, 1999.

CIE, 2001 a. CiE 1 42-2001 . Improvement to industrial colour-difference evaluation, 2001 .

CIE, 2001b. CIE DS 012:2001 . Standard method of assessing the spectral quality of daylight
simulators for visual appraisal and measurement of colour, 2001 .

CIE, 2004a. CIE DS 014-2.2:2004 Coiorimetry- Part 2: CIE Standard Illuminants, 2004.

CIE, 2004b. CIE 159:2004. A colour appearance model for colour management systems:
CIECAM02, 2004.

DIN, 2003. DIN 6176:2003. Colorimetric determination of colour differences of surface colours
using the DIN 99 formula, 2003.

FAIRMAN, H.S., 1985. The calculation of weight factors for tristimulus integration. Color Res,
AppL, 10, 199-203, 1985.

GUNDLACH, D., MALLWiTZ, E., 1976. Fragen der Probenbeleuchtung und MeSgeometrie in
der Farbmessung. Die Farbe : 25, 1 13-130, 1976.

JIS, 1991. JIS 8716. Fluorescent lamp as a simulator of CIE standard illuminant D 65 for a
visual comparison of surface colours - Type and characteristics, 1991 .

JUDD, D.B., MACADAM, D.L, WYSZECKI, G., 1964. with the collaboration of BUDDE, H.W.,
CONDIT, H.R., HENDERSON, ST., SIMONDS, J.L. Spectral distribution of typical daylight as
a function of correlated color temperature. J. Opt. Soc. Am. 54, 1031-1040, 1964.

LE GRAND, Y., 1968. Light, Colour and Vision. Second Edition. London, Chapman and Hall,
1-564, 1968.

28

CI E 15:2004

Li, C.J., LUO, M.R., R!GG, B., 2004. A new method for computing optimum weights for
calculating CIE Tristimulus Values. Color Res. AppL, 29, 91-103, 2004.

MCLAREN, K., 1980. CIELAB hue-angle anomalies at low tristimulus ratios. Color Res. AppL,
5, 139-143, 1980.

PAULI, H, 1976. Proposed extension of the CIE recommendation on "Uniform color spaces,
color difference equations, and metric color terms". J. Opt. Soc. Am., 66, 866-867, 1976.

ROBERTSON, A.R., 1968. Computation of correlated color temperature and distribution
temperature. J. Opt Soc. Am., 58, 1528-35, 1968.

ROBERTSON, A.R., 1978. CIE guidelines for coordinated research on colour difference
evaluation. Color Res. AppL, 3, 149-151, 1978.

SEVE, R., 1991. New formula for the computation of CiE 1976 hue difference. Color Res.
AppL, 16, 217-218, 1991.

SEVE, R., 1996. Practical formula for the computation of CIE 1976 hue difference. Color Res.
AppL, 21, 314, 1996.

SEVE, R., DUVAL, B., 2003. Interpolation procedure: Proposals and comments. In CIE
152:2003, Proc. CIE 25 th Session Vol. 1. D1 -74-77, 2003.

STOKES, M., BRILL, M.H., 1992. Efficient computation of AH* ab . Color Res. AppL, 17, 410-
411, 1992.

VENABLE, W.H., 1989. Accurate tristimulus values from spectral data. Color Res. AppL, 14,
260-267, 1989.

WYSZECKi, G., 1968. Recent agreements reached by the Colorimetry Committee of the
Commission Internationale de i'Eclairage, J. Opt. Soc. Am., 58, 290-292, 1968.

WYSZECKI, G., STILES, W.S., 1982. Color Science - Concepts and Methods, Quantitative
Data and Formulae. 2nd Edition. New York, John Wiley & Sons, 1982.

29

C!E 15:2004

11.

TABLES

This Section of the report contains tables of abridged and truncated coiorimetric data. The full
tables - recommended for genera! use - are found in the CIE standards on co!orimetry xlv
The tables presented here are intended for use, only when the highest precision is not
required. Users should check before using these tables whether the level of precision meets
their needs.

The iiluminant tables in this section are provided for the range between 300 nm and
780 nm. The tables of other coiorimetric functions are provided for the range between 380 nm
and 780 nm. All tables are at 5 nm intervals.

11.1 Table T.1. Relative spectral power distributions of CIE illuminants

Relative spectral power distributions [S(A)] of CIE standard illuminants A and D65, as well as
CIE illuminants C, D50, D55 and D75 for wavelengths X = 300 nm to 780 nm at 5 nm
intervais xv

A, nm

Standard

Iiluminant A

Standard
iiluminant D65

Iiluminant
C

Iiluminant
D50

Iiluminant
D55

Iiluminant
D75

300

0,930 483

0,034 100

0,00

0,019

0,024

0,043

305

1,12821

1 ,664 30

0,00

1,035

1,048

2,588

310

1,357 69

3,294 50

0,00

2,051

2,072

5,133

315

1,622 19

11,765 2

0,00

4,914

6,648

17,470

320

1,925 08

20,236

0,01

7,778

1 1 ,224

29,808

325

2,269 80

28,644 7

0,20

11,263

15,936

42,369

330

2,659 81

37,053 5

0,40

14,748

20,647

54,930

335

3,098 61

38,501 1

1,55

16,348

22,266

56,095

340

3,589 68

39,948 8

2,70

17,948

23,885

57,259

345

4,136 48

42,430 2

4,85

19,479

25,851

60,000

350

4,742 38

44,91 1 7

7,00

21,010

27,817

62,740

355

5,410 70

45,775

9,95

22,476

29,219

62,861

360

6,144 62

46,638 3

12,90

23,942

30,621

62,982

365

6,947 20

49,363 7

17,20

25,451

32,464

66,647

370

7,821 35

52,089 1

21,40

26,961

34,308

70,312

375

8,769 80

51,032 3

27,50

25,724

33,446

68,507

380

9,795 10

49,975 5

33,00

24,488

32,584

66,703

385

10,899 6

52,311 8

39,92

27,179

35,335

68,333

390

12,085 3

54,648 2

47,40

29,871

38,087

69,963

395

13,354 3

68,701 5

55,17

39,589

49,518

85,946

400

14,708

82,754 9

63,30

49,308

60,949

101,929

405

16,148

87,120 4

71,81

52,910

64,751

106,911

410

17,675 3

91,486

80,60

56,513

68,554

111,894

415

19,290 7

92,458 9

89,53

58,273

70,065

112,346

420

20,995

93,431 8

98,10

60,034

71,577

112,798

XIV These tables can also be found on the accompanying CD-ROM.

xv Standard iiluminant A and standard iiluminant D65 data are every fifth value from the CIE
Standard. The iiluminant C data are unchanged from CIE 15.2-1986. The D50, D55 and D75
data are calculated according to the present version of CIE 15.

30

CiE 15:2004

X, nm

Standard
Illuminant A

Standard
Illuminant D65

Illuminant
C

Illuminant
D50

Illuminant
D55

Illuminant
D75

425

22,788 3

90,057

105,80

58,926

69,746

107,945

430

24,670 9

86,682 3

112,40

57,818

67,914

103,092

435

26,642 5

95,773 6

117,75

66,321

76,760

112,145

440

28,702 7

104,865

121,50

74,825

85,605

121,198

445

30,850 8

110,936

123,45

81,036

91,799

127,104

450

33,085 9

117,008

124,00

87,247

97,993

133,010

455

35,406 8

117,410

123,60

88,930

99,228

132,682

460

37,812 1

117,812

123,10

90,612

100,463

132,355

465

40,300 2

116,336

123,30

90,990

100,188

129,838

470

42,869 3

114,861

123,80

91,368

99,913

127,322

475

45,517 4

115,392

124,09

93,238

101,326

127,061

480

48,242 3

115,923

123,90

95,109

102,739

126,800

485

51,041 8

112,367

122,92

93,536

100,409

122,291

490

53,913 2

108,811

120,70

91,963

98,078

117,783

495

56,853 9

109,082

116,90

93,843

99,379

117,186

500

59,861 1

109,354

112,10

95,724

100,680

116,589

505

62,932

108,578

106,98

96,169

100,688

115,146

510

66,063 5

107,802

102,30

96,613

100,695

113,702

515

69,252 5

106,296

98,81

96,871

100,341

111,181

520

72,495 9

104,790

96,90

97,129

99,987

108,659

525

75,790 3

106,239

96,78

99,614

102,098

109,552

530

79,132 6

107,689

98,00

102,099

104,210

110,445

535

82,519 3

106,047

99,94

101,427

103,156

108,367

540

85,947

104,405

102,10

100,755

102,102

106,289

545

89,412 4

104,225

103,95

101,536

102,535

105,596

550

92,912

104,046

105,20

102,317

102,968

104,904

555

96,442 3

102,023

105,67

101,159

101,484

102,452

560

100,000

100,000

105,30

100,000

100,000

100,000

565

103,582

98,167 1

104,11

98,868

98,608

97,808

570

107,184

96,334 2

102,30

97,735

97,216

95,616

575

110,803

96,061 1

100,15

98,327

97,482

94,914

580

114,436

95,788

97,80

98,918

97,749

94,213

585

118,080

92,236 8

95,43

96,208

94,590

90,605

590

121,731

88,685 6

93,20

93,499

91,432

86,997

595

125,386

89,345 9

91,22

95,593

92,926

87,112

600

129,043

90,006 2

89,70

97,688

94,419

87,227

605

132,697

89,802 6

88,83

98,478

94,780

86,684

610

136,346

89,599 1

88,40

99,269

95,140

86,140

615

139,988

88,648 9

88,19

99,155

94,680

84,861

620

143,618

87,698 7

88,10

99,042

94,220

83,581

625

147,235

85,493 6

88,06

97,382

92,334

81,164

630

150,836

83,288 6

88,00

95,722

90,448

78,747

31

CIE 15:2004

X, nm

Standard
llluminant A

Standard
llluminant D65

llluminant
C

llluminant
D50

llluminant
D55

llluminant
D75

635

154,418

83,493 9

87,86

97,290

91,389

78,587

640

157,979

83,699 2

87,80

98,857

92,330

78,428

645

161,516

81,863

87,99

97,262

90,592

76,614

650

165,028

80,026 8

88,20

95,667

88,854

74,801

655

168,510

80,120 7

88,20

96,929

89,586

74,562

660

171,963

80,214 6

87,90

98,190

90,317

74,324

665

175,383

81,246 2

87,22

100,597

92,133

74,873

670

178,769

82,277 8

86,30

103,003

93,950

75,422

675

182,118

80,281

85,30

101,068

91,953

73,499

680

185,429

78,284 2

84,00

99,133

89,956

71,576

685

188,701

74,002 7

82,21

93,257

84,817

67,714

690

191,931

69,721 3

80,20

87,381

79,677

63,852

695

195,118

70,665 2

78,24

89,492

81,258

64,464

700

198,261

71,609 1

76,30

91,604

82,840

65,076

705

201,359

72,979

74,36

92,246

83,842

66,573

710

204,409

74,349

72,40

92,889

84,844

68,070

715

207,411

67,976 5

70,40

84,872

77,539

62,256

720

210,365

61,604

68,30

76,854

70,235

56,443

725

213,268

65,744 8

66,30

81,683

74,768

60,343

730

216,120

69,885 6

64,40

86,511

79,301

64,242

735

218,920

72,486 3

62,80

89,546

82,147

66,697

740

221,667

75,087

61,50

92,580

84,993

69,151

745

224,361

69,339 8

60,20

85,405

78,437

63,890

750

227,000

63,592 7

59,20

78,230

71,880

58,629

755

229,585

55,005 4

58,50

67,961

62,337

50,623

760

232,115

46,418 2

58,10

57,692

52,793

42,617

765

234,589

56,611 8

58,00

70,307

64,360

51,985

770

237,008

66,805 4

58,20

82,923

75,927

61,352

775

239,370

65,094 1

58,50

80,599

73,872

59,838

780

241,675

63,382 8

59,10

78,274

71,818

58,324

32

CI E 15:2004

1 1 .2 Table T\2> Components S (A), S^A), S 2 (/l)

Components S Q (X), Si(A), S 2 (A) of daylight used in the calculation of relative spectral power
distributions of CIE daylight illuminants of different correlated colour temperatures, for
wavelengths X = 300 nm to 830 nm at 5 nm intervals.

A, nm

S (A)

Si(A)

S 2 (A)

300

0,04

0,02

0,00

305

3,02

2,26

1,00

310

6,00

4,50

2,00

315

17,80

13,45

3,00

320

29,60

22,40

4,00

325

42,45

32,20

6,25

330

55,30

42,00

8,50

335

56,30

41,30

8,15

340

57,30

40,60

7,80

345

59,55

41,10

7,25

350

61,80

41,60

6,70

355

61,65

39,80

6,00

360

61,50

38,00

5,30

365

65,15

40,20

5,70

370

68,80

42,40

6,10

375

66,10

40,45

4,55

380

63,40

38,50

3,00

385

64,60

36,75

2,10

390

65,80

35,00

1,20

395

80,30

39,20

0,05

400

94,80

43,40

-1,10

405

99,80

44,85

-0,80

410

104,80

46,30

-0,50

415

105,35

45,10

-0,60

420

105,90

43,90

-0,70

425

101,35

40,50

-0,95

430

96,80

37,10

-1,20

435

105,35

36,90

-1,90

440

113,90

36,70

-2,60

445

119,75

36,30

-2,75

450

125,60

35,90

-2,90

455

125,55

34,25

-2,85

460

125,50

32,60

-2,80

465

123,40

30,25

-2,70

470

121,30

27,90

-2,60

475

121,30

26,10

-2,60

480

121,30

24,30

-2,60

485

117,40

22,20

-2,20

X, nm

S (A)

SiW)

S 2 {X)

490

113,50

20,10

-1,80

495

113,30

18,15

-1,65

500

113,10

16,20

-1,50

505

111,95

14,70

-1,40

510

110,80

13,20

-1,30

515

108,65

10,90

-1,25

520

106,50

8,60

-1,20

525

107,65

7,35

-1,10

530

108,80

6,10

-1,00

535

107,05

5,15

-0,75

540

105,30

4,20

-0,50

545

104,85

3,05

-0,40

550

104,40

1,90

-0,30

555

102,20

0,95

-0,15

560

100,00

0,00

0,00

565

98,00

-0,80

0,10

570

96,00

-1,60

0,20

575

95,55

-2,55

0,35

580

95,10

-3,50

0,50

585

92,10

-3,50

1,30

590

89,10

-3,50

2,10

595

89,80

-4,65

2,65

600

90,50

-5,80

3,20

605

90,40

-6,50

3,65

610

90,30

-7,20

4,10

615

89,35

-7,90

4,40

620

88,40

-8,60

4,70

625

86,20

-9,05

4,90

630

84,00

-9,50

5,10

635

84,55

-10,20

5,90

640

85,10

-10,90

6,70

645

83,50

-10,80

7,00

650

81,90

-10,70

7,30

655

82,25

-11,35

7,95

660

82,60

-12,00

8,60

665

83,75

-13,00

9,20

670

84,90

-14,00

9,80

675

83,10

-13,80

10,00

33

CIE 15:2004

A, nm

SoU)

Si(A)

S 2 (A)

680

81,30

-13,60

10,20

685

76,60

-12,80

9,25

690

71,90

-12,00

8,30

695

73,10

-12,65

8,95

700

74,30

-13,30

9,60

705

75,35

-13,10

9,05

710

76,40

-12,90

8,50

715

69,85

-11,75

7,75

720

63,30

-10,60

7,00

725

67,50

-11,10

7,30

730

71,70

-11,60

7,60

735

74,35

-11,90

7,80

740

77,00

-12,20

8,00

745

71,10

-11,20

7,35

750

65,20

-10,20

6,70

755

56,45

-9,00

5,95

760

47,70

-7,80

5,20

A, nm

SoW

Sitf)

S 2 (A)

765

58,15

-9,50

6,30

770

68,60

-11,20

7,40

775

66,80

-10,80

7,10

780

65,00

-10,40

6,80

785

65,50

-10,50

6,90

790

66,00

-10,60

7,00

795

63,50

-10,15

6,70

800

61,00

-9,70

6,40

805

57,15

-9,00

5,95

810

53,30

-8,30

5,50

815

56,10

-8,80

5,80

820

58,90

-9,30

6,10

825

60,40

-9,55

6,30

830

61,90

-9,80

6,50

34

CIE 15:2004

1 1 .3 Table T.3. Tristimuius values, chromaticity coordinates of CIE illuminants

Tristimulus values, X, V, Z, and chromaticity coordinates x, y, and u\ v' for CIE standard
illuminants A and D65, as well as for CIE iiluminants C, D50, D55 and D75 computed for the
1931 and 1964 standard colorimetric observers.

1. For the CIE 1931 standard colorimetric observer as defined in Table T.4 and illuminants
as defined in Table T.1 (5 nm intervals over the range 380 nm to 780 nm).

Standard
llluminant A

Standard

llluminant

D65

llluminant
C

llluminant
D50

llluminant
D55

llluminant
D75

X

109,85

95,04

98,07

96,42

95,68

94,97

Y

100,00

100,00

100,00

100,00

100,00

100,00

Z

35,58

108,88

118,22

82,51

92,14

122,61

X

0,447 58

0,312 72

0,310 06

0,345 67

0,332 43

0,299 03

y

0,407 45

0,329 03

0,316 16

0,358 51

0,347 44

0,314 88

u'

0,255 97

0,197 83

0,200 89

0,209 16

0,204 43

0,193 53

V'

0,524 29

0,468 34

0,460 89

0,488 08

0,480 75

0,458 53

2. For the CIE 1964 standard colorimetric observer as defined in Table T.5 and illuminants
as defined in Table T.1 (5 nm intervals over the range 380 nm to 780 nm).

Standard
llluminant A

Standard
llluminant D65

llluminant
C

llluminant
D50

llluminant
D55

llluminant
D75

X10

111,14

94,81

97,29

96,72

95,80

94,42

Vio

100,00

100,00

100,00

100,00

100,00

100,00

Z10

35,20

107,32

116,14

81,43

90,93

120,64

*10

0,451 17

0,313 81

0,310 39

0,347 73

0,334 12

0,299 68

yio

0,405 94

0,330 98

0,319 05

0,359 52

0,348 77

0,317 40

u'io

0,258 96

0,197 86

0,200 00

0,210 15

0,205 07

0,193 05

v'w

0,524 25

0,469 54

0,462 55

0,488 86

0,481 65

0,460 04

35

CIE 15:2004

11.4 Table T.4. CIE 1931 standard colorimetric observer

Truncated set of colour-matching functions x(/L), y(A), z(X) and corresponding chromaticity

coordinates x(A), y(A) for wavelengths X = 380 nm to 780 nm at 5 nm intervals, rounded to 6
and 5 decimal places respectively. Vi

Z, nm

X(Z)

yW

zW

x(X)

M

380

0,001 368

0,000 039

0,006 450

0,174 11

0,004 96

385

0,002 236

0,000 064

0,010 550

0,174 01

0,004 98

390

0,004 243

0,000 120

0,020 050

0,173 80

0,004 92

395

0,007 650

0,000 217

0,036 210

0,173 56

0,004 92

400

0,014 310

0,000 396

0,067 850

0,173 34

0,004 80

405

0,023 190

0,000 640

0,110 200

0,173 02

0,004 78

410

0,043 510

0,001 210

0,207 400

0,172 58

0,004 80

415

0,077 630

0,002 180

0,371 300

0,172 09

0,004 83

420

0,134 380

0,004 000

0,645 600

0,171 41

0,005 10

425

0,214 770

0,007 300

1,039 050

0,170 30

0,005 79

430

0,283 900

0,011 600

1,385 600

0,168 88

0,006 90

435

0,328 500

0,016 840

1 ,622 960

0,166 90

0,008 56

440

0,348 280

0,023 000

1,747 060

0,164 41

0,010 86

445

0,348 060

0,029 800

1,782 600

0,161 10

0,013 79

450

0,336 200

0,038 000

1,772 110

0,156 64

0,017 70

455

0,318 700

0,048 000

1,744 100

0,150 99

0,022 74

460

0,290 800

0,060 000

1,669 200

0,143 96

0,029 70

465

0,251 100

0,073 900

1,528 100

0,135 50

0,039 88

470

0,195 360

0,090 980

1,287 640

0,124 12

0,057 80

475

0,142 100

0,112 600

1,041 900

0,109 59

0,086 84

480

0,095 640

0,139 020

0,812 950

0,091 29

0,132 70

485

0,057 950

0,169 300

0,616 200

0,068 71

0,200 72

490

0,032 010

0,208 020

0,465 180

0,045 39

0,294 98

495

0,014 700

0,258 600

0,353 300

0,023 46

0,412 70

500

0,004 900

0,323 000

0,272 000

0,008 17

0,538 42

505

0,002 400

0,407 300

0,212 300

0,003 86

0,654 82

510

0,009 300

0,503 000

0,158 200

0,013 87

0,750 19

515

0,029 100

0,608 200

0,111 700

0,038 85

0,812 02

520

0,063 270

0,710 000

0,078 250

0,074 30

0,833 80

525

0,109 600

0,793 200

0,057 250

0,114 16

0,826 21

530

0,165 500

0,862 000

0,042 160

0,154 72

0,805 86

535

0,225 750

0,914 850

0,029 840

0,192 88

0,781 63

540

0,290 400

0,954 000

0,020 300

0,229 62

0,754 33

545

0,359 700

0,980 300

0,013 400

0,265 78

0,724 32

550

0,433 450

0,994 950

0,008 750

0,301 60

0,692 31

XVi Chromaticity coordinates have been calculated from the non-rounded values published in
(CIE, 1986a).

36

CiE 15:2004

Z, nm

x(X)

VW

Z{X)

m

y(A)

555

0,512 050

1,000 000

0,005 750

0,337 36

0,658 85

560

0,594 500

0,995 000

0,003 900

0,373 10

0,624 45

565

0,678 400

0,978 600

0,002 750

0,408 74

0,589 61

570

0,762 100

0,952 000

0,002 100

0,444 06

0,554 71

575

0,842 500

0,915 400

0,001 800

0,478 77

0,520 20

580

0,916 300

0,870 000

0,001 650

0,512 49

0,486 59

585

0,978 600

0,816 300

0,001 400

0,544 79

0,454 43

590

1,026 300

0,757 000

0,001 100

0,575 15

0,424 23

595

1,056 700

0,694 900

0,001 000

0,602 93

0,396 50

600

1,062 200

0,631 000

0,000 800

0,627 04

0,372 49

605

1,045 600

0,566 800

0,000 600

0,648 23

0,351 39

610

1,002 600

0,503 000

0,000 340

0,665 76

0,334 01

615

0,938 400

0,441 200

0,000 240

0,680 08

0,319 75

620

0,854 450

0,381 000

0,000 190

0,691 50

0,308 34

625

0,751 400

0,321 000

0,000 100

0,700 61

0,299 30

630

0,642 400

0,265 000

0,000 050

0,707 92

0,292 03

635

0,541 900

0,217 000

0,000 030

0,714 03

0,285 93

640

0,447 900

0,175 000

0,000 020

0,719 03

0,280 93

645

0,360 800

0,138 200

0,000 010

0,723 03

0,276 95

650

0,283 500

0,107 000

0,000 000

0,725 99

0,274 01

655

0,218 700

0,081 600

0,000 000

0,728 27

0,271 73

660

0,164 900

0,061 000

0,000 000

0,729 97

0,270 03

665

0,121 200

0,044 580

0,000 000

0,731 09

0,268 91

670

0,087 400

0,032 000

0,000 000

0,731 99

0,268 01

675

0,063 600

0,023 200

0,000 000

0,732 72

0,267 28

680

0,046 770

0,017 000

0,000 000

0,733 42

0,266 58

685

0,032 900

0,011 920

0,000 000

0,734 05

0,265 95

690

0,022 700

0,008 210

0,000 000

0,734 39

0,265 61

695

0,015 840

0,005 723

0,000 000

0,734 59

0,265 41

700

0,011 359

0,004 102

0,000 000

0,734 69

0,265 31

705

0,008 111

0,002 929

0,000 000

0,734 69

0,265 31

710

0,005 790

0,002 091

0,000 000

0,734 69

0,265 31

715

0,004 109

0,001 484

0,000 000

0,734 69

0,265 31

720

0,002 899

0,001 047

0,000 000

0,734 69

0,265 31

725

0,002 049

0,000 740

0,000 000

0,734 69

0,265 31

730

0,001 440

0,000 520

0,000 000

0,734 69

0,265 31

735

0,001 000

0,000 361

0,000 000

0,734 69

0,265 31

740

0,000 690

0,000 249

0,000 000

0,734 69

0,265 31

745

0,000 476

0,000 172

0,000 000

0,734 69

0,265 31

750

0,000 332

0,000 120

0,000 000

0,734 69

0,265 31

755

0,000 235

0,000 085

0,000 000

0,734 69

0,265 31

760

0,000 166

0,000 060

0,000 000

0,734 69

0,265 31

37

CIE 15:2004

X, nm

X(X)

VW

*W

x(X)

yW

765

0,000 117

0,000 042

0,000 000

0,734 69

0,265 31

770

0,000 083

0,000 030

0,000 000

0,734 69

0,265 31

775

0,000 059

0,000 021

0,000 000

0,734 69

0,265 31

780

0,000 042

0,000 015

0,000 000

0,734 69

0,265 31

Summation at 5 nm intervals:

£*P) = 21 ,371524 J^yW = 21,371327 ^W :

21,371 540

11.5 Table T.5. CIE 1964 standard colorimetric observer

Truncated set of colour-matching functions x w (X), y w (A), z w (X) and chromaticity

coordinates x 10 (A), y^{x) for wavelengths X ~ 380 nm to 780 nm at 5 nm intervals, rounded to
6 decimal places and 5 decimal places respectively xv ".

A,nm

*ioU)

yioW

*ioW

X 10 (/L)

yio(^)

380

0,000 160

0,000 017

0,000 705

0,181 33

0,019 69

385

0,000 662

0,000 072

0,002 928

0,180 91

0,019 54

390

0,002 362

0,000 253

0,010 482

0,180 31

0,019 35

395

0,007 242

0,000 769

0,032 344

0,179 47

0,019 04

400

0,019 110

0,002 004

0,086 011

0,178 39

0,018 71

405

0,043 400

0,004 509

0,197 120

0,177 12

0,018 40

410

0,084 736

0,008 756

0,389 366

0,175 49

0,018 13

415

0,140 638

0,014 456

0,656 760

0,173 23

0,017 81

420

0,204 492

0,021 391

0,972 542

0,170 63

0,017 85

425

0,264 737

0,029 497

1,282 500

0,167 90

0,018 71

430

0,314 679

0,038 676

1,553 480

0,165 03

0,020 28

435

0,357 719

0,049 602

1,798 500

0,162 17

0,022 49

440

0,383 734

0,062 077

1 ,967 280

0,159 02

0,025 73

445

0,386 726

0,074 704

2,027 300

0,155 39

0,030 02

450

0,370 702

0,089 456

1,994 800

0,151 00

0,036 44

455

0,342 957

0,106 256

1,900 700

0,145 94

0,045 22

460

0,302 273

0,128 201

1,745 370

0,138 92

0,058 92

465

0,254 085

0,152 761

1,554 900

0,129 52

0,077 87

470

0,195 618

0,185 190

1,317 560

0,115 18

0,109 04

475

0,132 349

0,219 940

1,030 200

0,095 73

0,159 09

480

0,080 507

0,253 589

0,772 125

0,072 78

0,229 24

485

0,041 072

0,297 665

0,570 060

0,045 19

0,327 54

490

0,016 172

0,339 133

0,415 254

0,020 99

0,440 11

495

0,005 132

0,395 379

0,302 356

0,007 30

0,562 52

XV!I Chromaticity coordinates have been calculated from the non-rounded values published in
(CIE, 1986a).

38

CI E 15:2004

A, nm

X 10 (A)

y^W

Z 10 (A)

X10W)

y-ioW

500

0,003 816

0,460 777

0,218 502

0,005 59

0,674 54

505

0,015 444

0,531 360

0,159 249

0,021 87

0,752 58

510

0,037 465

0,606 741

0,112 044

0,049 54

0,802 30

515

0,071 358

0,685 660

0,082 248

0,085 02

0,816 98

520

0,117 749

0,761 757

0,060 709

0,125 24

0,810 19

525

0,172 953

0,823 330

0,043 050

0,166 41

0,792 17

530

0,236 491

0,875 211

0,030 451

0,207 06

0,766 28

535

0,304 213

0,923 810

0,020 584

0,243 64

0,739 87

540

0,376 772

0,961 988

0,013 676

0,278 59

0,711 30

545

0,451 584

0,982 200

0,007 918

0,313 23

0,681 28

550

0,529 826

0,991 761

0,003 988

0,347 30

0,650 09

555

0,616 053

0,999 110

0,001 091

0,381 16

0,618 16

560

0,705 224

0,997 340

0,000 000

0,414 21

0,585 79

565

0,793 832

0,982 380

0,000 000

0,446 92

0,553 08

570

0,878 655

0,955 552

0,000 000

0,479 04

0,520 96

575

0,951 162

0,915 175

0,000 000

0,509 64

0,490 36

580

1,014 160

0,868 934

0,000 000

0,538 56

0,461 44

585

1 ,074 300

0,825 623

0,000 000

0,565 44

0,434 56

590

1,118 520

0,777 405

0,000 000

0,589 96

0,410 04

595

1,134 300

0,720 353

0,000 000

0,611 60

0,388 40

600

1,123 990

0,658 341

0,000 000

0,630 63

0,369 37

605

1,089 100

0,593 878

0,000 000

0,647 13

0,352 87

610

1,030 480

0,527 963

0,000 000

0,661 22

0,338 78

615

0,950 740

0,461 834

0,000 000

0,673 06

0,326 94

620

0,856 297

0,398 057

0,000 000

0,682 66

0,317 34

625

0,754 930

0,339 554

0,000 000

0,689 76

0,310 24

630

0,647 467

0,283 493

0,000 000

0,695 48

0,304 52

635

0,535 110

0,228 254

0,000 000

0,700 99

0,299 01

640

0,431 567

0,179 828

0,000 000

0,705 87

0,294 13

645

0,343 690

0,140 211

0,000 000

0,710 25

0,289 75

650

0,268 329

0,107 633

0,000 000

0,713 71

0,286 29

655

0,204 300

0,081 187

0,000 000

0,715 62

0,284 38

660

0,152 568

0,060 281

0,000 000

0,716 79

0,283 21

665

0,112 210

0,044 096

0,000 000

0,717 89

0,282 11

670

0,081 261

0,031 800

0,000 000

0,718 73

0,281 27

675

0,057 930

0,022 602

0,000 000

0,719 34

0,280 66

680

0,040 851

0,015 905

0,000 000

0,719 76

0,280 24

685

0,028 623

0,011 130

0,000 000

0,720 02

0,279 98

690

0,019 941

0,007 749

0,000 000

0,720 16

0,279 84

695

0,013 842

0,005 375

0,000 000

0,720 30

0,279 70

700

0,009 577

0,003 718

0,000 000

0,720 36

0,279 64

705

0,006 605

0,002 565

0,000 000

0,720 32 0,279 68

39

CIE 15:2004

A.nm

X 10 (2)

yioU)

Z10W

x 10 (A)

yio(>t)

710

0,004 553

0,001 768

0,000 000

0,720 23

0,279 77

715

0,003 145

0,001 222

0,000 000

0,720 09

0,279 91

720

0,002 175

0,000 846

0,000 000

0,719 91

0,280 09

725

0,001 506

0,000 586

0,000 000

0,719 69

0,280 31

730

0,001 045

0,000 407

0,000 000

0,719 45

0,280 55

735

0,000 727

0,000 284

0,000 000

0,719 19

0,280 81

740

0,000 508

0,000 199

0,000 000

0,718 91

0,281 09

745

0,000 356

0,000 140

0,000 000

0,718 61

0,281 39

750

0,000 251

0,000 098

0,000 000

0,718 29

0,281 71

755

0,000 178

0,000 070

0,000 000

0,717 96

0,282 04

760

0,000 126

0,000 050

0,000 000

0,717 61

0,282 39

765

0,000 090

0,000 036

0,000 000

0,717 24

0,282 76

770

0,000 065

0,000 025

0,000 000

0,716 86

0,283 14

775

0,000 046

0,000 018

0,000 000

0,716 46

0,283 54

780

0,000 033

0,000 013

0,000 000

0,716 06

0,283 94

Summation at 5 nm intervals:

]Tx 10 (A) = 23,329 353 ^]y 10 (A)- 23,332036 ]Tz 10 (2) -23,334153 !!

11.6 Table T.6. Relative spectral power distributions of illuminants representing
typical fluorescent lamps, for wavelengths 2=380nm to 780 nm at 5 nm
intervals

Table 7.6.1 Fluorescent lamps FL1-12, already published In CIE 15.2 as F1-F12 xvm .

FL1-6: standard; FL7-9: broad-band; FL10-12: narrow band fluorescent lamps.

X, nm

FL1

FL2*

FL3

FL4

FL5

FL6

FL7*

FL8

FL9

FL10

FL11*

FL12

380

1,87

1,18

0,82

0,57

1,87

1,05

2,56

1.21

0,90

1,11

0,91

0,96

385

2,36

1,48

1,02

0.70

2,35

1,31

3,18

1,50

1,12

0,80

0,63

0,64

390

2,94

1,84

1,26

0,87

2,92

1,63

3,84

1,81

1,36

0,62

0,46

0,40

395

3,47

2,15

1,44

0,98

3,45

1,90

4,53

2,13

1,60

0,57

0,37

0,33

400

5,17

3,44

2,57

2,01

5,10

3,11

6,15

3,17

2,59

1,48

1,29

1,19

405

19,49

15,69

14,36

13,75

18,91

14.80

19.37

13,08

12,80

12,16

12,68

12,48

410

6,13

3,85

2,70

1,95

6,00

3,43

7,37

3,83

3,05

2,12

1,59
1 79

1,12
0,94

415

6,24

3,74

2,45

1.59

6,11

3,30

7,05

3,45

2,56

2,70

420

7,01

4,19

2,73

1,76

6,85

3.68

7,71

3,86

2,86

3,74

2,46

1.08

425

7,79

4,62

3,00

1,93

7,58

4,07

8,41

4,42

3,30

5,14

3,33

1,37

430

8,56

5,06

3,28

2,10

8,31

4,45

9,15

5,09

3,82

6,75

4,49

1,78

435

43,67

34,98

31,85

30,28

40,76

32,61

44,14

34,10

32,62

34,39

33,94

29,05

440

16,94

11,81

9,47

8,03

16,06

10,74

17,52

12,42

10,77

14,86

12,13

7,90

xvm liiuminants FL2*, FL7* and FL11* should take priority over others when a few typical
fluorescent lamp illuminants are to be selected.

40

CIE 15:2004

a, nm

FL1

FL2*

FL3

FL4

FL5

FL6

FL7* FL8

FL9

FL10

FL11*

FL12

445

10,72

6,27

4,02

2,55

10,32

5,48

11,35

7,68

5,84

10,40

6,95

2,65

450

11,35

6,63

4,25

2,70

10,91

5,78

12,00

8,60

6,57

10,76

7,19

2,71

455

11,89

6,93

4,44

2,82

11,40

6,03

12,58

9,46

7,25

10,67

7,12

2,65

460

12,37

7,19

4,59

2,91

11,83

6 ; 25

13,08

10,24

7,86

10,11

6,72

2,49
2,33

465

12,75

7.40

4,72

2,99

12,17

6,41

13,45

10,84

8,35

9,27

6,13

470

13,00

7,54

4.80 3,04

12,40

6,52

13,71

11,33

8,75

8,29

5,46 | 2,10

475

13,15

7,62

4,86 i 3,08

12,54

6,58

13,88

11,71

9,06

7,29

4,79

1,91

480

13,23

7,65

4,87

3,09

12,58

6,59

13,95

11,98

9,31

7,91

5,66

3,01

485

13,17

7,62

4,85

3,09

12,52

6,56

13,93

12,17

9,48

16,64

14,29

10,83

490

13.13

7,62

4,88

3,14

12,47

6.56

13,82

12,28

9,61

16,73

14,96

11,88

495

12,85

7,45

4,77

3,06

12,20

6,42

13,64

12,32

9,68

10,44

8,97

6,88

500

12,52

7,28

4,67

3,00

11,89

6,28

13,43

12,35

9,74

5,94

4,72

3,43

505

12,20

7,15

4,62

2,98

11,61

6,20

13,25

12,44

9,88 | 3,34

2,33

1,49

510

11,83

7,05

4,62

3,01

11,33

6,19

13,08

12,55

10,04

2,35

1,47

0,92

515

11,50

7,04

4,73

3,14

11,10

6,30

12,93

12,68

10,26

1,88

1.10

0,71

520

11,22

7,16

4,99

3,41

10,96

6,60

12,78

12,77

10,48 | 1,59

0,89

0,60

525

530

11,05

7,47

5,48

3,90

10,97

7.12

12,60

12,72

10,63 | 1,47

0,83

0,63

11,03

8,04

6,25

4,69

11.16

7,94

12,44

12,60

10,78

1,80

1,18

1,10

535

11.18

8,88

7,34

5,81

11,54

9,07

12,33

12,43

10,96

5,71

4,90

4,56

540

11,53

10,01

8,78

7,32

12,12

10,49

12,26

12,22

11,18

40,98

39,59

34,40

545

27,74

24,88

23,82

22,59

27,78

25,22

29,52

28,96

27,71

73,69

72,84

65,40

550

17,05

16,64

16,14

15.11

17,73

17,46

17,05

16,51

16.29

33,61

32,61

29,48

555

13,55

14,59

14,59

13,88

14,47

15,63

12,44

11.79

12,28

8,24

7,52

7,16

560

14,33

16,16

16,63

16,33

15,20

17,22

12.58

11,76

12,74

3,38

2,83

3.08

565

15,01

17,56

18,49

18,68

15,77

18,53

12,72

11,77

13,21

2,47

1,96

2,47

570

15,52

18,62

19,95

20,64

16,10

19,43

12,83

11,84

13,65

2,14

1,67

2,27

575

18,29

21,47

23,11

24,28

18,54

21,97

15,46

14,61

16,57

4,86

4,43

5,09

580

19,55

22,79

24,69

26,26

19,50

23,01

16,75

16,11

18,14

11,45

11,28

11,96

585

15,48

19,29

21,41

23,28

15,39

19,41

12,83

12,34

14,55

14,79

14,76

15,32

590

14,91

18,66

20,85

22,94

14,64

18,56

12,67

12,53

14,65

12,16

12,73

14,27

595

14,15

17,73

19,93

22.14

13,72

17,42

12,45

12,72

14,66

8,97

9,74

11,86

600

13,22

16,54

18,67

20 91

12,69

16,09

12,19

12,92

14,61

6.52

7,33

9,28

605

12,19

15,21

17,22

19,43

11,57

14,64

11,89

13,12

14,50

8,31

9,72

12,31

610

11,12

13,80

15,65

17,74

10,45

13,15

11,60

13,34

14,39

44,12

55,27

68,53

615

10,03

12,36

14,04

16,00

9,35

11,68

11,35

13,61

14,40

34,55

42,58

53,02

620

! 8,95

10,95

12,45

14,42

8,29

10,25

11,12

13,87

14,47

12,09

13,18

14,67

625

I 7,96

9,65

10,95

12,56

7,32

8,95

10,95

14,07

14,62

12,15

13,16

14,38

630
635
640
645
650

7,02

8,40

9,51

10,93

6,41

7,74

10,76

14,20

14,72

10,52

12,26

14,71

6,20

7,32

8,27

9,52

5,63

6,69

10,42

14,16

14,55

4,43

5,11

6.46

5 42

6,31

7,11

8,18

4,90

5,71

10,11

14,13

14,40

1,95

2,07

2,57

4,73

5 43

6,09

7,01

4,26

4,87

10,04

14,34

14,58

2,19

2,34

2,75

4,15

4,68

5,22

6,00

3,72

4,16

10,02

14,50

14,88

3,19

3,58

4.18

41

CIE 15:2004

X, nm

FL1

FL2*

FL3

FL4

FL5

FL6

FL7*

FL8

FL9

FL10

FL11*

FL12

655

3,64

4,02

4,45

5,11

3,25

3,55

10,11

14,46

15,51

2,77

3,01

3,44

660

3,20

3,45

3,80

4,36

2.83

3,02

9,87

14,00

15,47

2,29

2,48

2,81

665

2.81

2,96

3,23

3,69

2,49

2,57

8,65

12,58

13,20

2,00

2,14

2,42

670

2,47

2,55

2,75

3,13

2,19

2,20

7.27

10,99

10,57

152

1,54

1,64

675

2,18

2,19

2,33

2,64

1,93

1,87

6,44

9,98

9,18

135

133

136

680

1,93

1,89

1,99

2,24

1,71

1,60

5,83

9,22

8,25

147

1,46

1,49

685

1,72

1,64

1,70

1,91

152

137

5,41

8,62

7,57

1,79

1,94

2,14

690

1.67

1,53

1.55

170

148

1,29

5,04

8,07

7,03

174

2,00

2,34

695

1,43

1,27

1,27

1,39

1,26

1,05

4,57

7,39

6,35

1,02

1,20

142

700

1,29

1 10

1,09

1,18

1,13

0,91

4,12

6,71

5,72

114

135

1,61

705

1,19

0,99

0,96

1,03

1,05

0,81

3,77

6,16

5,25

3,32

4.10

5,04

710

1,08

0,88

0,83

0,88

0,96

0,71

3,46

5,63

4,80

4,49

5,58

6,98

715

0,96

0,76

0.71

0,74

0,85

0,61

3,08

5,03

4,29

2,05

2.51

3,19

720

0,88

0,68

0,62

0.64

0,78

0,54

2,73

4,46

3,80

0,49

0,57

0,71

725

0,81

0,61

0.54

0,54

0,72

0,48

2.47

4,02

3,43

0,24

0,27

0,30

730

0.77

0,56

0,49

0,49

0,68

0,44

2,25

3,66

3,12

0,21

0,23

0,26

735

0,75

0,54

0,46

0,46

0,67

0,43

2,06

3,36

2,86

0,21

0,21

0,23

740

0,73

0,51

0,43

0,42

0,65

0,40

1,90

3,09

2,64

0.24

0,24

0,28

745

0,68

0.47

0,39

0,37

0,61

0,37

175

2,85

2,43

0,24

0,24

0,28

750

0,69

0,47

0,39

0,37

0,62

0,38

1,62

2,65

2,26

0,21

0,20

0,21

755

0.64

0,43

0,35

0,33

0,59

0,35

1,54
1,45

2,51

2,14

0,17

0,24

0,17

760

0,68

0,46

0,38

0,35

0,62

0,39

2,37

2,02

0,21

0,32

0,21

765

0,69

0,47

0,39

0,36

0,64

0,41

1,32

2,15

1,83

0,22

0,26

0,19

770

0,61

0,40

0,33

0.31

0,55

0,33

117

1,89

1,61

0,17

0,16

0,15

775

0,52

0,33

0,28

0,26

0,47

0,26

0,99

1,61

1,38

0,12

0,12

0,10

780

0,43

0,27

0,21

0.19

0,40

0,21

0.81

132

1,12

0,09

0,09

0,05

42

CI E 15:2004

Table T.6.2.a. New set of fluorescent lamps. FL3.1-3: Standard halophosphate lamps;
FL3.4-6: DeLuxe type lamps; FL3.7-8: Three band fluorescent iamps.

X, nm +

FL3.1

FL3.2

FL3.3

FL3.4

FL3.5

FL3.6

FL3.7

FL3.8

380

2,39

5,80

8,94

3,46

4,72

5,53

3,79

4,18

385

2,93

6,99

11,21

3,86

5,82

6,63

2,56

2,93

390

3,82

8,70

14,08

4,41

7,18

8,07

1,91

2,29

395

4,23

9,89

16,48

4,51

8,39

9,45

1,42

1,98

400

4,97

11,59

19,63

4,86

9,96

11,28

1,51

2,44

405

86,30

94,53

116,33

71,22

58,86

61,47

73,64

70,70

410

11,65

20,80

32,07

8,72

15,78

17,80

7,37

10,19

415

7,09

16,52

29,72

5,36

15,10

17,47

4,69

9,79

420

7,84

18,30

33,39

5,61

17,30

20,12

5,33

13,21

425

8,59

20,33

36,94

5,91

19,66

23,05

6,75

17,79

430

9,44

22,00

40,33

6,42

22,43

26,37

8,51

22,98

435

196,54

231,90

262,66

192,77

176,00

186,01

181,81

191,43

440

10,94

25,81

46,87

7,77

28,67

33,94

11,71

31,76

445

11,38

27,63

49,79

8,37

31,92

37,98

11,96

33,35

450

11,89

29,10

52,46

9,22

35,38

42,12

12,18

33,87

455

12,37

30,61

54,81

10,18

38,73

46,38

11,90

32,89

460

12,81

31,92

56,81

11,18

41,98

50,30

11,16

30,60

465

13,15

33,11

58,44

12,28

44,92

53,95

11,22

28,28

470

13,39

33,83

59,52

13,38

47,49

56,94

9,83

24,81

475

13,56

34,70

60,12

14,54

49,58

59,48

8,94

21,60

480

13,59

35,02

60,24

15,74

51,21

61,36

12,08

23,40

485

13,56

35,22

59,88

17,09

52,36

62,68

52,56

68,99

490

14,07

35,81

59,88

19,60

53,99

64,34

55,42

70,85

495

13,39

35,14

58,60

21,05

53,78

63,90

31,69

42,29

500

13,29

35,14

57,85

23,96

54,04

63,85

16,03

22,67

505

13,25

34,90

56,29

27,77

53,88

63,24

6,72

11,08

510

13,53

34,70

54,81

32,68

53,62

62,46

4.59

7,66

515

14,24

35,02

53,42

38,29

53,25

61,41

3,67

6,07

520

15,74

36,13

52,70

43,76

53,09

60,47

3,02

5,07

525

18,26

37,92

52,50

47,72

52,88

59,48

3,21

4,88

530

22,28

40,62

53,30

50,27

52,99

58,65

4,90

6,26

535

27,97

44,70

54,89

51,78

53,15

57,93

19,05

20,29

540

35,70

49,63

57,61

52,68

53,67

57,49

177,64

204,67

545

148.98

154,16

182,75

167,36

167,93

175,17

347,34

390,25

550

56,55

62,21

65,27

55,29

55,61

57,27

116,80

135,69

555

68,68

68,92

69,41

56,94

56,82

57,49

31,87

34,57

560

79,99

75,83

73,28

59,30

58,39

57,99

16,37

15,71

565

91,47

81,95

76,56

62,15

60,22

58,76

14,92

12,60

570

101,32

86,95

78,67

65,26

62,21

59,64

14,12

11,05

575

123,16

103,54

95,74

84,26

81,45

78,77

29,50

25,05

580

129,53

109,94

97,22

89,22

84,96

81,26

61,40

54,98

585

115,05

91,95

76,79

75,79

68,71

63,18

85,05

82,84

43

C!E 15:2004

X, nm +

FL3.1

FL3.2

FL3.3

FL3.4

FL3.5

FL3.6

FL3.7

FL3.8

590

113,48

89,85

73,36

79,19

70,70

64,29

64,86

58,22

595

110,08

87,15

69,33

82,80

73,01

65,78

65,01

53,06

600

104,28

83,26

64,23

85,76

74,69

66,77

53,17

41,44

605

97,98

78,93

58,92

88,62

76,26

67,77

34,22

25,26

610

89,60

73,93

53,38

91,12

77,68

68,60

427,27

329,89

615

80,74

68,84

47,91

93,43

78,67

69,10

201,10

161,29

620

71,92

63,44

42,61

96,89

80,14

70,15

58,63

54,19

625

63,50

58,84

37,74

101,45

81,71

71,69

72,01

66,30

630

55,46

53,84

33,11

103,65

82,08

71,97

88,19

71,43

635

47,97

49,43

29,04

100,30

79,98

69,81

20,07

15,74

640

41,39

45,54

25,29

97,89

78,15

68,05

13,10

10,22

645

35,50

41,53

22,10

96,59

76,52

66,66

12,92

10,68

650

30,32

38,31

19,31

106,21

79,20

69,70

24,54

20,32

655

25,79

34,62

16,84

109,97

79,51

70,37

15,94

14,13

660

21,84

31,80

14,68

117,49

81,08

72,47

13,56

11,72

665

18,53

29,02

12,89

96,04

7076

62,30

13,38

11,75

670

15,67

26,72

11,37

80,15

62,58

54,45

8,42

7,87

675

13,22

24,22

9,97

70,42

56,87

49,20

6,57

6,38

680

11,14

22,19

8,82

65,01

52,83

45,60

7,18

7,23

685

9,40

20,41

7,86

60,15

49,11

42,40

9,90

8,94

690

8,65

19,10

7,78

56,04

46,28

40,02

11,47

9,79

695

6,75

16,79

6,30

50,92

42,24

36,48

8,88

7,26

700

5,69

15,13

5,67

46,26

38,58

33,28

3.05

2,59

705

4,87

13,82

5,15

42,60

35,59

30,84

22,04

17,03

710

4,29

12,63

4,91

38,85

32,76

23,30

42,79

33,69

715

3,54

11,39

4,31

35,09

29,61

25,65

14,40

12,02

720

3,03

10,32

3,99

31,73

26,89

23,33

1,88

1,68

725

2,62

9,21

3,67

28,77

24,53

21,23

1,60

1,50

730

2,28

8,89

3,43

25,76

22,17

19,29

1,42

1,31

735

1,94

7,50

3,19

23,16

20,02

17,41

1,05

1,01

740

1,70

6,71

2,95

21,30

18,45

16,31

1,23

1,16

745

1,50

6,11

2,75

18,55

16,09

14,21

1,76

1,59

750

1,36

5,40

2,63

17,74

15,62

14,04

0,74

0,79

755

1,16

4,80

2,43

14,74

13,10

11,55

0,52

0,67

760

4,91

8,70

7,14

12,93

11,69

10,39

4,10

4,82

765

0,95

4,01

2,19

13,63

12,42

11,28

0,46

0,61

770

1,50

4,09

2,71

10,43

9,43

8,51

0,99

1,25

775

0,89

3,30

2,00

9,67

8,96

8,24

0,43

0,79

780

0,68

2,82

1,80

8,07

7,39

7,02

0,00

0,58

+ This table gives the representative data of these lamps only in the 380 nm to 780 nm
region for colorimetric purposes, though many fluorescent lamps emit power outside this
spectral region, especially in the near ultraviolet. Other sources of data must be consulted if
information is required below 380 nm or above 780 nm.

44

CiE 15:2004

Table T.6.2b. New set of fluorescent lamps, cont FL3.9-11: Three band fluorescent lamps;
FL3.12-14: Multi-band fluorescent lamps; FL3.15: D65 simulator lamp.

X, nm + [ FL3.9

FL3.10

FL3.11

FL3.12

FL3.13

FL3.14

FL3.15

380

3,77

0,25

3,85

1,62

2,23

2,87

300,00

385

2,64

2,91

2,06

2,92

3,69

286,00

390

2,06

2,56

2,71

3,91

4,87

268,00

395

1,87

2,59

3,11

4,55

5,82

244,00

400

2,55

0,69

3,63

3,67

5,46

7,17

304,00

405

71,68

21,24

74,54

74,60

77,40

72,21

581,00

410

12,05

2,18

14,69

8,88

11,25

13,69

225,00

415

13,57

1,86

17,22

4,77

7,69

11,12

155,00

420

19,60

3,1

24,99

4,72

8,29

12,43

152,00

425

27,33

5

34,40

4,72

8,98

13,90

170,00

430

35,39

7,03

44,57

4,94

10,01

15,82

295,00

435

211,82

45,08

228,08

150,29

204,45

200,99

1 417,00

440

49,02

16,78

61,53

6,08

13,75

21,72

607,00

445

51,83

12,28

65,31

7,13

16,88

26,33

343,00

450

52,50

13,31

66,35

9,10

21,73

32,85

386,00

455

50,73

13,66

64,37

11,76

27,96

40,80

430,00

460

46,93

13,69

59,81

14,96

34,92

49,23

469,00

465

42,42

13,13

54,24

18,54

41,96

57,39

502,00

470

37,16

12,28

47,42

22,48

48,62

65,26

531,00

475

31,84

11,42

41,10

26,76

54,33

71,99

552,00

480

31,94

11,66

40,04

31,66

59,49

78,25

567,00

485

77,74

22,04

85,54

40,93

67,91

88,85

572,00

490

79,45

26,17

86,55

45,83

70,01

91,67

575,00

495

47,93

18,57

53,47

46,00

66,40

86,81

561,00

500

26,24

11,36

30,91

45,26

62,07

80,42

548,00

505

13,15

6,83

17,41

43,16

56,95

73,82

527,00

510

8,80

5,58

12,56

41,63

52,70

69,12

507,00

515

6,70

4,88

10,10

39,75

48,54

63,69

482,00

520

5,38

4,31

8,48

37,83

44,80

58,44

461,00

525

4,93

3,76

7,74

36,16

41,75

53,57

438,00

530

6,06

3,61

8,58

35,25

39,77

49,66

418,00

535

19,76

5,62

21,39

37,04

40,50

48,44

404,00

540

215,94

38,59

220,12

59,86

59,27

72,56

429,00

545

412,13

100

417,35

183,53

184,09

200,42

1016,00

550

142,39

36,54

146,13

59,03

59,06

65,00

581,00

555

34,74

10,57

36,67

47,93

49,95

47,49

370,00

560

14,76

2,98

16,51

48,67

50,90

44,14

368,00

565

10,99

2,05

12,56

52,69

54,51

44,71

371,00

570

9,25

1,84

10,81

57,24

58,33

46,01

377,00

575

23,50

6,09

25,31

77,75

77,49

63,52

490,00

580

53,05

17,27

53,31

87,81

85,78

71,73

525,00

585

81,90

21,77

80,75

80,55

76,20

63,52

402,00

45

CIE 15:2004

X, nm +

FL3.9

FL3.10

FL3.11

FL3.12

FL3.13

FL3.14

FL3.15

590

54,92

18,72

53,56

84,83

78,73

64,13

404,00

595

47,80

10,15

44,02

86,84

78,95

63,74

412,00

600

36 } 65

7,26

33,05

91,44

81,48

66,82

418,00

605

21,82

5,17

20,26

96,51

84,57

70,65

425,00

610

285,69

56,66

233,61

105,25

87,75

79,29

428,00

615

139,94

49,39

118,20

106,74

89,56

80,77

432,00

620

53,37

18.57

51,66

108,53

91,36

83,59

433,00

625

64,30

14,21

61,27

106,92

89,00

82,59

431,00

630

64,04

14,01

55,15

101,54

83,67

77,60

427,00

635

13,79

5,99

12,95

95,20

78,26

72,47

420,00

640

9,06

2,68

8,93

89,34

73,19

68,34

410,00

645

9,83

3,14

9,77

82,95

67,61

63,82

399,00

650

18,60

6.25

17,12

75,78

61,42

58,57

385,00

655

13,38

5,78

13,01

68,65

55,49

53,18

370,00

660

10,99

6,75

10,45

61,70

49,78

47,97

352,00

665

10,77

5,16

10,33

55,23

44,46

43,14

336,00

670

7,57

3,03

7,70

48,58

39,13

38,19

317,00

675

6,19

1,57

6,34

42,90

34,45

33,85

298,00

680

7,09

1,72

7,35

37,74

30,28

29,94

277,00

685

8,54

1,54

8,22

32,93

26,37

26,24

260,00

690

8,77

1,71

7,93

29,65

23,88

23,90

242,00

695

6,41

1,1

5,70

25,19

20,10

20,33

223,00

700

2,26

0,28

2,23

21,69

17,40

17,42

202,00

705

15,02

3,65

12,43

19,28

15,29

15,64

187,00

710

29,39

7,54

24,24

17,36

13,62

14,34

167,00

715

10,22

2,34

8,74

14,74

11,68

12,21

152,00

720

1,42

0,05

1,39

12,86

10,31

10,65

136,00

725

1,23

0,04

1,23

11,28

9,11

9,43

125,00

730

1,10

0,04

1,10

9,97

8,03

8,34

113,00

735

0,84

0,03

0,84

8,88

7,13

7,52

103,00

740

0,97

0,03

0,94

7,78

6,31

6,73

93,00

745

1,35

0,02

1,23

7,04

5,67

6,08

84,00

750

0,65

0,02

0,68

6,30

5,11

5,52

75,00

755

0,13

0,01

0,52

5,55

4,55

5,00

66,00

760

4,22

0,01

4,60

10,15

9,06

9,47

58,00

765

0,10

0,45

4,50

3,74

4,08

51,00

770

0,68

1,04

4,81

4,04

4,43

46,00

775

0,16

0,45

3,72

3,14

3,39

41,00

780

0,00

0,00

3,28

2,75

3,17

37,00

+ This table gives the representative data of these lamps only in the 380 nm to 780 nm
region for coiorimetric purposes, though many fluorescent lamps emit power outside this
spectral region, especially in the near ultraviolet. Other sources of data must be consulted if
information is required below 380 nm or above 780 nm.

46

CI E 15:2004

11.7 Table T.7. High pressure discharge lamps. HP1: Standard high pressure sodium
lamp; HP2: Colour enhanced high pressure sodium Samp; HP3-5: Three types of
high pressure metal halide lamps

X, nm +

HP1

HP2

HP3

HP4

HP5

380

1,90

2,64

3,15

9,80

0,34

385

2,20

2,77

7,49

13,30

7,11

390

2,50

3,42

10,87

19,97

11,49

395

2,70

3,68

12,57

25,81

14,97

400

3,10

4,33

12,97

24,69

14,95

405

4,30

5,50

21,29

47,66

29,14

410

3,80

5,94

26,29

54,44

38,08

415

4,20

7,20

30,18

63,82

51,56

420

4,80

9,02

43,06

85,52

62,56

425

5,19

10,27

29,58

60,54

55,61

430

5,89

12,48

23,18

38,37

41,98

435

7,39

16,82

35,28

88,20

50,02

440

7,89

16,04

26,29

44,94

42,14

445

5,69

15,26

24,29

35,64

39,04

450

12,89

22,58

22,91

30,75

40,52

455

6,69

20,07

26,20

33,77

45,29

460

4,30

15,13

29,31

40,81

51,01

465

20,78

25,27

25,30

33,77

49,18

470

12,99

28,04

28,14

35,28

49,05

475

6,69

15,99

24,05

32,55

46,12

480

1,40

10,40

21,82

29,44

45,73

485

1,50

11,10

20,51

26,16

39,46

490

3,20

13,44

23,05

29,96

44,39

495

18,18

22,62

26,98

32,83

46,14

500

56,24

49,71

30,96

33,58

49,54

505

2,90

17,21

30,72

41,16

59,76

510

2,10

17,12

27,13

32,93

48,47

515

13,39

27,26

29,55

32,13

48,38

520

2,10

20,02

34,22

34,45

48,70

525

2,00

21,54

29,98

30,12

44,25

530

2,20

23,36

41,21

41,13

54,42

535

2,30

25,66

173,14

187,10

128,93

540

2,60

29,69

141,37

101,37

81,26

545

5,10

43,12

64,98

123,96

67,36

550

11,39

98,30

33,83

42,47

48,48

555

15,48

125,60

34,26

34,73

51,41

560

20,78

134,57

33,32

31,82

48,88

565

55,64

149,70

52,80

54,67

68,52

570

254,03

166,12

74,29

57,45

80,85

575

56,14

98,77

47,97

70,43

65,96

580

111,78

30,47

49,20

69,50

59,43

47

CIE 15:2004

A, nm +

HP1

HP2

HP3

HP4

HP5

585

297,98

1,17

96,07

49,37

67,57

590

142,55

0,39

85,41

183,35

128,34

595

334,84

1,65

175,18

162,15

131,85

600

189,40

21,41

153,73

109,35

101,70

605

117,78

76,11

120,22

72,38

77,05

610

79,92

126,16

98,90

70,60

66,27

615

108,09

161,96

90,22

58,08

77,09

620

46,85

160,06

70,07

44,13

60,51

625

38,16

158,19

66,84

50,20

65,23

630

32,47

153,69

57,61

40,80

57,86

635

28,37

147,40

53,03

37,91

56,20

640

25,37

140,60

49,85

36,71

54,32

645

22,98

134,92

48,16

38,30

56,34

650

20,38

127,59

42,76

31,24

45,74

655

19,78

124,65

50,64

35,31

50,79

660

17,78

118,02

48,42

45,62

56,66

665

16,78

113,94

41,27

35,82

51,99

670

19,18

118,10

43,44

89,91

84,31

675

17,98

115,16

40,48

36,01

47,48

680

13,69

102,85

35,16

32,57

47,46

685

9,99

90,54

34,94

39,26

61,78

690

8,19

83,34

24,68

23,27

34,51

695

7,59

79,44

24,70

25,30

38,74

700

6,99

76,97

21,49

20,02

30,98

705

6,79

74,85

19,49

17,54

25,45

710

6,49

73,12

18,48

16,25

22,88

715

6,39

71,51

17,55

15,20

20,82

720

6,09

70,13

17,36

15,15

21,05

725

5,99

69,04

17,09

15,22

20,81

730

5,79

67,48

16,32

14,26

18,69

735

5,79

66,70

16,07

12,63

17,54

740

5,79

66,31

16,58

14,75

19,58

745

5,79

65,14

15,78

13,19

16,42

750

6,39

65,70

17,66

17,63

23,77

755

5,99

64,79

20,46

23,38

35,39

760

5,59

64,10

16,59

16,02

21,37

765

31,97

83,04

17,81

24,46

34,58

770

27,87

86,25

16,07

22,05

30,21

775

5,89

63,93

14,83

16,11

19,71

780

6,69

64,92

14,61

12,91

15,61

* The relative spectral power distribution of the HP-illuminants given here can only be used
over the spectral range from 380 nm to 780 nm. Although many high pressure gas discharge
lamps emit power outside this spectral range, especially in the near ultraviolet, other sources
of data must be consulted if information is required below 380 nm or above 780 nm.

48

CiE 15:2004

1 1 .8 Table T.8. Colorimetric data for the fluorescent lamp illuminants of Table T.6

Table T. 8.1. Illuminants as published in Table T.6. 1.

Lamp

Chromaticity coordinates
x y

Correlated colour

temperature, (T cp )

(kelvlns)

General colour
rendering index, R a

FL1

0,3131

0,3371

6430

76

FL2

0,3721

0,3751

4230

64

FL3

0,4091

0,3941

3450

57

FL4

0,4402

0,4031

2940

51

FL5

0,3138

0,3452

6350

72

FL6

0,3779

0,3882

4150

59

FL7

0,3129

0,3292

6500

90

FL8

0,3458

0,3586

5000

95

FL9

0,3741

0,3727

4150

90

FL 10

0,3458

0,3588

5000

81

FL11

0,3805

0,3769

4000

83

FL12

0,4370

0,4042

3000

83

Table T.8.2. Illuminants as published in Table T.6. 2.

FL3.1

FL3.2

FL3.3

FL3.4

FL3.5

FL3.6

FL3.7

x~

0,4407

0,3808

0,3153

; 4429

0,3749

0,3488

0,4384

y=

0,4033

0,3734

0,3439

0,4043

0,3672

0,36

0,4045

7"cp=

2932 K

3965 K

6280 K

2904 K

4086 K

4894 K

2979 K

Special Rendering Indexes:

No. 1 =

42

65

64

91

97

97

97

No. 2 =

69

80

80

89

97

97

94

No. 3 =

89

89

89

79

92

93

54

No. 4 =

39

66

69

88

94

97

88

No. 5 =

41

66

69

88

97

97

86

No. 6 =

52

71

74

82

95

95

81

No. 7 =

66

79

81

88

94

96

87

No. 8 =

13

48

49

89

94

96

64

No. 9 =

-109

-37

-63

76

88

93

-9

No. 10 =

29

51

52

69

90

90

51

No. 11 =

19

56

62

88

95

97

76

No. 12 =

21

59

68

63

90

92

50

No. 13 =

47

68

68

91

97

98

98

No. 14 =

93

94

93

87

95

95

69

General Colour Rendering index

*a =

51

70

72

87

95

96

82

49

CIE 15:2004

Table T.8.2 cont. Illuminants as published in Tabie T.6.2.

FL3.8

FL3.9

FL3.10

FL3.11

FL3.12

FL3.13

FL3.14

FL3.15

X-

0,382

0,3499

0,3455

0,3245

0,4377

0,383

0,3447

0,3127

y=

0,3832

0,3591

0,356

0,3434

0,4037

0,3724

0,3609

0,3288

7"c P =

4006 K

4853 K

5000 K

5854 K

2984 K

3896 K

5045 K

6509 K

Special Rendering Indices

No. 1 =

94

94

99

90

95

98

93

99

No. 2 =

89

89

97

86

98

97

94

99

No. 3 =

50

48

63

49

92

98

97

96

No. 4 =

85

84

92

82

95

97

94

98

No. 5 =

83

84

92

81

94

99

94

99

No. 6 =

73

72

85

70

97

97

93

100

No. 7 =

86

85

92

85

93

94

97

98

No. 8 =

72

78

86

79

83

88

97

98

No. 9 =

5

22

46

24

58

71

93

96

No. 10 =

40

38

62

34

88

99

91

99

No. 1 1 =

68

68

78

64

93

94

95

100

No. 12 =

48

51

72

50

85

89

85

95

No. 13 =

95

95

97

90

97

99

92

98

No. 14 =

67

66

75

67

94

98

97

98

General Colour Rendering Index

R* =

79

79

88

78

93

96

95

98

11.9 Table T.9. Colorimetric data for the high pressure illuminants of Table T.7

HP1

HP2

HP3

HP4

HP5

x=

0,533

0,4778

0,4302

0,3812

0,3776

y=

0,415

0,4158

0,4075

0,3797

0,3713

^

1959 K

2506 K

3144 K

4002 K

4039 K

Special Rendering Indices

No. 1 =

-3

98

87

75

87

No. 2 =

61

89

92

85

94

No. 3 =

40

73

87

84

97

No. 4 =

-27

89

89

78

89

No. 5 =

-4

88

85

75

89

No. 6 =

52

71

90

79

94

No. 7 =

21

81

82

77

85

No. 8 =

-75

72

50

42

64

No. 9 =

-260

52

-29

-60

10

No. 10 =

43

66

71

56

85

No. 11 =

-52

66

89

77

90

No. 12 =

27

55

72

64

90

No. 13 =

7

90

90

79

90

No. 14 =

61

82

91

91

98

General Colour Rendering Index

Ra =

8

83

83

74

87

50

CI E 15:2004

11.10 Table T.10. Values of the first deviation function used in the calculation of the
observer metamerism index

X, nm

Ax(i)

Ay(A)

Az(A)

380

-0,0001

0,0000

-0,0002

385

-0,0003

0,0000

-0,0010

390

-0,0009

-0,0001

-0,0036

395

-0,0026

-0,0004

-0,0110

400

-0,0069

-0,0009

-0,0294

405

-0,0134

-0,0015

-0,0558

410

-0,0197

-0,0019

-0,0820

415

-0,0248

-0,0022

-0,1030

420

-0,0276

-0,0021

-0,1140

425

-0,0263

-0,0017

-0,1079

430

-0,0216

-0,0009

-0,0872

435

-0,0122

0,0005

-0,0455

440

-0,0021

0,0015

^0,0027

445

0,0036

0,0008

0,0171

450

0,0092

-0,0003

0,0342

455

0,0186

-0,0005

0,0703

460

0,0263

-0,0011

0,0976

465

0,0256

-0,0036

0,0859

470

0,0225

-0,0060

0,0641

475

0,0214

-0,0065

0,0547

480

0,0205

-0,0060

0,0475

485

0,0197

-0,0045

0,0397

490

0,0187

-0,0031

0,0319

495

0,0167

-0,0037

0,0228

500

0,0146

-0,0047

0,0150

505

0,0133

-0,0059

0,0117

510

0,0118

-0,0060

0,0096

515

0,0094

-0,0025

0,0062

520

0,0061

0,0010

0,0029

525

0,0017

0,0005

0,0005

530

-0,0033

-0,001 1

-0,0012

535

-0,0085

-0,0020

-0, 0020

540

-0,0139

-0,0028

-0,0022

545

-0,0194

-0,0039

-0,0024

550

-0,0247

-0,0044

-0,0024

555

-0,0286

-0,0027

-0,0021

560

-0,0334

-0,0022

-0,0017

565

-0,0426

-0,0073

-0,0015

570

-0,0517

-0,0127

-0,0014

575

-0,0566

-0,0129

-0,0013

580

-0,0600

-0,0126

-0,0013

/L, nm

Ax(A)

Ay(Z)

Az{Z)

585

-0,0637

-0,0162

-0,001 1

590

-0,0656

-0,0196

-0,0009

595

-0,0638

-0,0199

-0,0008

600

-0,0595

-0,0187

-0,0006

605

-0,0530

-0,0170

-0,0005

610

-0,0448

-0,0145

-0,0004

615

-0,0346

-0,0112

0,0000

620

-0,0242

-0,0077

0,0002

625

-0,0155

-0,0048

0.0000

630

-0,0085

-0,0025

-0,0002

635

-0,0044

-0,0012

-0,0002

640

-0,0019

-0,0006

0,0000

645

-0,0001

0,0000

0,0000

650

0,0010

0,0003

0,0000

655

0,0016

0,0005

0,0000

660

0,0019

0,0006

0,0000

665

0,0019

0,0006

0,0000

670

0,0017

0,0006

0,0000

675

0,0013

0,0005

0,0000

680

0,0009

0,0003

0,0000

685

0,0006

0,0002

0,0000

690

0,0004

0,0001

0,0000

695

0,0003

0,0001

0,0000

700

0,0002

0,0001

0,0000

705

0,0001

0,0000

0,0000

710

0,0001

0,0000

0,0000

715

0,0001

0,0000

0,0000

720

0,0000

0,0000

0,0000

725

0,0000

0,0000

0,0000

730

0,0000

0,0000

0,0000

735

0,0000

0,0000

0,0000

740

0,0000

0,0000

0,0000

745

0,0000

0,0000

0,0000

750

0,0000

0,0000

0,0000

755

0,0000

0,0000

0,0000

760

0,0000

0,0000

0,0000

765

0,0000

0,0000

0,0000

770

0,0000

0,0000

0,0000

775

0,0000

0,0000

0,0000

780

0,0000

0,0000

0,0000

51

CIE 15:2004

APPENDIX A. OLD RECOMMENDATIONS, NOW OBSOLETE, AS WELL AS
REFERENCES TO NON-CIE COLOUR DIFFERENCE FORMULAE

Appendix A.1. llluminant B and Source B

llluminant B

This illuminant was intended to represent direct sunlight with a correlated colour temperature
of approximately 4900 K.

Source B

llluminant B was realized by source A, combined with a filter consisting of a layer, one
centimetre thick, of each of two solutions B^ and B 2 , contained in a double cell made of
colourless optical glass. The solutions were made up as follows:

Solution B1:

Copper Sulphate (CuS0 4 ■ 5H 2 0)

Mannite [C 6 H 8 (OH) 6 ]

Pyridine (C 5 H 5 N)

Distilled water to make
Solution B2:

Cobalt Ammonium Sulphate [CoS0 4 ) (NH 4 ) 2 S0 4 - 6H 2 0)]

Copper Sulphate (CuS0 4 .- 5H 2 0)

Sulphuric Acid (density 1,835 g*ml" 1 )

Distilled water to make

Appendix A.2. llluminant C and Source C

llluminant C

Representing average daylight with a correlated colour temperature of about 6800 K. The
spectral power distribution of llluminant C is reproduced in Table T.1.

Note: In Table T.1 the values for 775 nm and 780 nm have been added by extrapolation.

Source C

llluminant C is to be realized by source A, combined with a filter consisting of a layer, one
centimetre thick, of each of two solutions C-, and C 2 , contained in a double cell made of
colourless optical glass. The solutions are to be made up as follows:

Solution C1:

Copper Sulphate (CuS0 4 • 5H 2 0)
Mannite C 6 H 8 (OH) 6
Pyridine (C 5 H 5 N)
Distilled water to make
Solution C2:

Cobalt Ammonium Sulphate [CoS0 4 . (NH 4 ) 2 S0 4 . 6H 2 0] 30,58
Copper Sulphate (CuS0 4 . 5H 2 0)
Sulphuric Acid (density 1 ,835 g-ml" 1 )
Distilled water to make

2,452

g

2,452

g

30,0

ml

1000,0

ml

21,71

g

16,11

g

10,0

ml

1000,0

ml

3,412

g

3,412

g

30,0

ml

1000,0

mi

D] 30,58

g

22,52

g

10,0

ml

1000,0

ml

52

CI E 15:2004

Appendix A.3. CiE 1964 uniform colour space and colour difference formula

u, v uniform chromaticity scale (CIE 1960 UCS) diagram

This approximately uniform chromaticity diagram was produced by plotting
u = 4X/(X+ 15Y+ 3Z) as abscissa and v = 6YI(X+ 15/+ 3Z) as ordinate; wand vare related
to u' and \/ of the CIE 1976 UCS diagram by the equations u = u' and v= 2v73.

7964 uniform space and colour difference formula

This approximately uniform colour space was produced by plotting along three orthogonal
axes

W = 25Y 1/3 -17

U* = \ZW {u - u n )

\/* = 13W*(v-v n )

The associated colour difference formula was:

A£ = [((/*! - U* 2 ) 2 + (\T 1 - V* 2 f + (l/L^ - IV* 2 ) 2 ] 1/2

The coordinates in this system bear the following approximate relationships to the
coordinates of the CiELUV space:

U* = u*

V* = 2/3 v*

Appendix A.4. CIE 1994 colour difference formula (CIE94)

Based on the work documented in CIE 101-1993 (CIE, 1993), where experiments are
described that pointed out that a number of external parameters of a visual task affect the
correlation of visual magnitude judgements of colour differences with their colorimetric
measures, CIE started investigations with carefully selected data sets and reported a new
colour-difference formula that introduced weighting factors to the lightness, chroma and hue
differences, AL*, AC* ab and AH* ab , of the CIELAB - formula. The resulting recommendation
was as follows (CIE, 1995):

AF* -

ACT 94 ~

\2

AL*

f .. +\ 'AC* 1 ( AH'

k L S L

_a*L, m

^C^C J I ^H^H

The weighting functions, S L , S c , S H adjust the internal non-uniform structure of the
CIELAB - formula using

S L =1

S c = 1 + 0,045 C* ab

S H = 1 + 0,015 C* ab

If the standard of a sample pair is not clearly defined, C* ab may be replaced by the
geometric mean (C* abi1 • C* abi2 ) 1/2 .

Note 1: The parametric factors, k L , k c , k h are correction terms for variation in experimental
conditions. Under reference conditions they are all set at 1 . For other choices see
(CIE, 1993).

Note 2: An alternative colour difference formula used by some ISO committees, but never
endorsed by CIE is briefly described in Appendix A. 5.

Note 3: The CIE 1994 colour difference formula is now obsolete and has been superseded by
the CIEDE2000 formula.

53

C!E 15:2004

Appendix A.5. CMC(l:c) colour difference formula

The Colour Measurement Committee of the Society of Dyers and Colourists (UK)
recommended a coiour difference formula that has been integrated into some ISO standards.
It is a forerunner to CIE94 and was a model for developing the CIE94 formula. The main
deviations from CIE94 are found in the weighting factors that are much more complicated
mathematically in that they contain hue-dependent correction terms. They are defined as
follows (Clarke etal., 1984):

S L = 0,040 975 L^/(1 + 0,01 7 65 Lf) t unless L^ < 1 6 when S L = 0,511
S c = 0,063 8 C* a w!{-\ + 0,013 1 C* abi1 ) + 0,638
SH = S c (7f+1-/)
where

^={(C*ab,l) 4 /[(C*ab,l) 4 + 1900]} 1/2

7= 0,36 + I 0,4 cos (/) abi1 + 35) |
unless fr ab1 is between 164° and 345° when

7=0,56+ | 0,2 cos (/)ab,i +168)1
The parametric factors are defined as follows:

k t = l

k Q ~c

*h=1

The parametric factors are mostly chosen c = 1 and / varied between 1 and 2. The
choice of / and c must be indicated by setting the right numbers in the name of the formula,
e.g. for textiles a choice of CMC(2:1) is in common use.

CIE recommends the use of the CIEDE2000 formula whenever in the past the CIE 94
or CMC formula were used XiX

Appendix A.6. DIN99 coiour difference formuia

The preceding colour difference formulae including the CIEDE2000 coiour difference formula
are non-vectorial transformations from CIELAB space, and do not define a space for colour
differences. A new formula for colour differences was developed to cope with this problem:
the DIN99 colour difference formula published in DIN 6176 Coforimetric determination of
colour differences of surface colours using the DIN 99 formula (DIN, 2003).

References

CIE, 1993. CIE 101-1993. Parametric effects in coiour difference evaluation, 1993.

CIE, 1995. CIE 116-1995. industrial coiour difference evaluation, 1995.

CLARKE, F.J.J. , MCDONALD, R. and RIGG, B., 1984. Modification to the JPC79 colour
difference formula. J.Soc.Dyers Col. 100, 128-131, 1984.

DIN, 2003. DIN 6176. Colorimetric determination of colour differences of surface colours
using the DIN 99 formula, 2003.

XiX The recommended use of CIEDE2000 is in agreement with the persons who developed
the CMC formula.

54

CIE 15:2004

APPENDIX B. DEFINITIONS OF THE 7{A\ g(A), b(A ) COLOUR-MATCHING FUNCTIONS,
THE CIE RGB SYSTEM AND THE DERIVATION OF THE CiE XYZ SYSTEM FROM THE
CIE RGB SYSTEM FOR THE 1931 STANDARD OBSERVER

The colour-matching functions x{A),y(A), z(A) were originally derived from colour-matching
functions 7(X),g{A) 1 b(A:) referring to spectral reference stimuli [R], [G], [B]. These reference
stimuli were specified as stimuli of wavelengths 700,0 nm, 546,1 nm, and 435,8 nm,
respectively. Their units were chosen to make a mixture of equal quantities of the three
reference stimuli match the equi-energy spectrum. The luminances of the units of the three
spectral stimuli were in the ratios 1 ,0000 : 4,5907 : 0,0601 .

Appendix B.1. Determination of the 7(A), g(l), b(A) colour-matching functions

This determination results from two conventions originally adopted in 1931 .

The first convention was to adopt the ratios of the luminance of the reference colour
stimuli [R], [G], [B] as values.

The second convention was to attribute to the monochromatic stimuli constituting the
colour-matching functions a luminance equal to the spectral luminous efficiency V(A).

It follows from these conventions that

1 ,0000 7(X) + 4,5907 g(A) + 0,0601 b(A) = V(A) B.1

Since for any stimulus

R/r=G/g = B/b = L/l B.2

where / is the characteristic luminance of the chromaticity whose expression for
monochromatic stimuli reads

((A) = 1 ,00000 r{A) + 4,5907 g(A) + 0,0601 b(A) B.3

it follows that, with L = V(A)

7(A) = [ftA)V(A)]/l(Al g(X) = [g(A)V(A)]HW, b(A)=[b(AJV(A)]/l(Al B.4

These colour-matching functions as well as the corresponding chromaticity
coordinates, are given in Table B.1 .

The colour-matching functions x(A), y(A), z(?J) given in Table T.4 agree closely
with those defined originally in 1931. Three minor changes have been introduced. If rounded
to four decimal places, at A =775 nm the new value of x(2)is 0,0001 instead of 0,0000; at

A- 555 nm y(A)is 1,0000 instead of 1,0002; and at A - 740 nm y(A)\$ 0,0002 instead of
0,0003. These changes are considered insignificant in most colorimetric calculations.

It has been realized at an early stage that the 1924 V(A) function is too low in the blue
part of the spectrum, A corrected V M (A) function has been officially accepted by the CIE in
1988 (CIE, 1990). However, the X(A), Y(A), Z(A) colour-matching functions have not been
modified. A CIE Technical Committee is currently investigating the question of obtaining
visually meaningful colour-matching functions, see e.g. (Schanda, 1998).

55

CIE 15:2004

Appendix B.2. Derivation of the CIE XYZ trichromatic system from the CIE RGB
trichromatic system

The derivation of the XYZ system from the RGB system had to fulfil a certain number of
requirements. Their fulfilment led to the establishment of a set of three linear equations
relating the reference stimuli [X], [Y], [Z] to the reference stimuli [R], [G], [B] as follows:

[X] = 0,418 455 [R] - 0,091 165 [G] + 0,000 921 [B]

[Y] = -0,158 657 [R] + 0,252 426 [G] - 0,002 550 [B] B.5

[Z] = -0 ; 082 832 [R] + 0,015 705 [G] +0,178 595 [B]

Another set of three linear equations yield, for any stimulus, the tristimulus values X,
Y, Z as function of the tristimulus values R, G, B:

X= 2,768 892 R + 1,751 748 G + 1,130 160 B

Y = 1 ,000 000 R + 4,590 700 G + 0,060 1 00 B B.6

Z = + 0,056 508 G + 5,594 292 B

These sets B. 5 and B. 6 are not independent, each one may be mathematically
derived from the other. The set B. 6 was developed first and its coefficients are exact values
(Morren, 2000), This set may be considered as more appropriate in the present context, but
the set B. 5 is more basic, Since colour-matching functions are a particular case of tristimulus
values, the set B. 6 gives directly three equations providing x(A), y(X), z(A) as a function of

The second of these equations:

y(A) =1,000 000 r(A) + 4,590 700 g(X) + 0,060 100 b{A)

is particularly interesting: it reproduces the left-hand side of equation B. 1 under Section B. 1
and thus immediately leads to y{X) = V(A).

Note: However, the same conclusion may be obtained by considering other features of the
XYZ system. The transformation between reference stimuli attributes to the
luminance L Y the value 1. Moreover, since the reference stimuli [X] and [Z] are
located on the alychne of the system, leading to L x = L z = 0, one has for any stimulus

L = Y and l-y B.7

Consequently, equations similar to B. 4 lead to

x(/)=[x(l).l/(l)]/yW, y(X) = V(Al z(A) - [z(l)-\/(A)]/y(A) B.8

These expressions are simpler than those given by the set B. 6.

In deriving the CIE XYZ colorimetric system a fundamental criterion was to link the
system to photometry. The units of the RGB system, the RGB primaries, were already
determined by their luminance. Furthermore this was done by using a transformation from the
RGB system to the XYZ system where y(Z) became equivalent to V(A), determined by flicker
photometry. Although y(X) was intended to be a brightness correlate, it is actually a

luminance correlate, i.e. it does not describe the brightness relationship between coloured
lights. It does, however, provide a good estimate for the visibility of fine detail.

56

CI E 15:2004

Appendix B.3. Definition of the colour-matching functions in the CIE 1964 trichromatic
system

The colour-matching functions x 10 (A), y 10 W, *ioW deff n ' n 9 the CIE 1964 standard
coiorimetric observer given in Table T.5 were derived from colour-matching functions referring
to matching stimuli [R 10 ], [G 10 ], [B 10 ]. These are stimuli specified in terms of wavenumbers (v)
15 500 cm" 1 , 19 000 cm" 1 , and 22 500 cm" 1 (corresponding approximately to wavelengths
645,2 nm, 526,3 nm, and 444,4 nm), and their amounts are given in power units.

The three reference stimuli [R 10 ], [G 10 J, [B 10 ] have the same power and the colour-
matching functions r 10 (v), g<\ (v), b w (v) are defined as monochromatic stimuli whose power
equates to that of the reference stimuli. The r 10 (v) , g 10 (v) , j£) 10 (v) colour matching functions
are reproduced in Table B.2.

The derivation of the [X 10 ], [Y 10 ], [Z 10 ] system from the [R 10 ], [G 10 ], [B 10 ] system is
based on principles that lead to a coordinate system similar to the system associated with the
CIE 1931 standard coiorimetric observer. The following transformation equations relate very
closely the r 10 (v), g 10 M, b w (v) values of Table B. 2 to x 10 (k), y 10 (v), z 10 (v) values:

x 10 (v) = 0,341 080 r 10 (v) + 0,189 145 g 10 (v) + 0,387 529 b 10 (v)
y 10 (v) - 0,139 058 r 10 (v) + 0,837 460 g 10 (v) + 0,073 316 b w (v)
z 10 (v) - 0,000 000 r 10 (w) + 0,039 553 g 10 (v) 4 2,026 200 b w (v)

Chromaticity coordinates x 10 (v), yi ( v), z^(v) were then computed from
x 10 M= * 1oM

^oM+yioM+^oM

y 10 (v)= M

^oM + yioM + ^oM

z 10 (v)

Table 2 of CIE standard coiorimetric observers (CIE, 1986) contains the official
colour-matching functions x 10 (/l) , y 10 (A), z 10 (^) and chromaticity coordinates x 10 (^) t y 10 (^),
z 10 (/L) on a wavelength basis obtained by interpolation and extrapolation of the functions
XioM - 7io(^) ' *ioM and x io(^). yioU), z 10 (/t) at intervals of 1 nm. Table T.5 contains every
fifth value of this table.

The above transformation equations deviate somewhat from those originally
published (CIE, 1959), which related the unsmoothed values of r w (v), g 10 (v), b 10 (v) with
the unsmoothed values of x 10 (A) , y 10 (^) , z w (Jl) . The values published in CIE 15.2 (Table
2.6) are reproduced in this Appendix as Table B. 2.

In deriving the CIE 1964 standard coiorimetric observer no direct photometric
measurements were required. The large-field colour matching data as defined by the CIE
1964 standard coiorimetric observer are intended to apply to matches where the luminance
and relative spectral power distributions of the matched stimuli are such that no participation
of the rod receptors of the visual mechanism is to be expected. This condition of observation
is important as "rod intrusion" may upset the predictions of the standard observer.

In obtaining the RGB-XYZ transformation CIE tried to get the y 10 (^) function as near
as possible to a 10 degree spectral luminosity function based on flicker photometry. The CIE
is currently investigating the possibility of introducing on this basis a V^ (X) function.

57

CIE 15:2004

Table B.1 . Colour-matching functions r(X ), g{ X ), b(X ) and corresponding chromaticity

coordinates r{A), 9(a), b(X) for wavelength 380 nm to 780 nm at 5 nm intervals for
the 1931 standard observer.

X, nm

7(X)

9W

b(X)

tXX)

gU)

b(X)

380

0,00003

-0,00001

0,00117

0,0272

-0,0115

0,9843

385

0,00005

-0,00002

0,00189

0,0268

-0,0114

0,9846

390

0,00010

-0,00004

0,00359

0,0263

-0,0114

0,9851

395

0,00017

-0,00007

0,00647

0,0256

-0,0113

0,9857

400

0,00030

-0,00014

0,01214

0,0247

-0,0112

0,9865

405

0,00047

-0,00022

0,01969

0,0237

-0,01 1 1

0,9874

410

0,00084

-0,00041

0,03707

0,0225

-0,0109

0,9884

415

0,00139

-0,00070

0,06637

0,0207

-0,0104

0,9897

420

0,00211

-0,00110

0,11541

0,0181

-0,0094

0,9913

425

0,00266

-0,00143

0,18575

0,0142

-0,0076

0,9934

430

0,00218

-0,00119

0,24769

0,0088

-0,0048

0,9960

435

0,00036

-0,00021

0,29012

0,0012

-0,0007

0,9995

440

-0,00261

0,00149

0,31228

-0,0084

0,0048

1,0036

445

-0,00673

0,00379

0,31860

-0,0213

0,0120

1,0093

450

-0,01213

0,00678

0,31670

-0,0390

0,0218

1,0172

455

-0,01874

0,01046

0,31166

-0,0618

0,0345

1,0273

460

-0,02608

0,01485

0,29821

-0,0909

0,0517

1,0392

465

-0,03324

0,01977

0,27295

-0,1281

0,0762

1,0519

470

-0,03933

0,02538

0,22991

-0,1821

0,1175

1,0646

475

-0,04471

0,03183

0,18592

-0,2584

0,1840

1,0744

480

-0,04939

0,03914

0,14494

-0,3667

0,2906

1,0761

485

-0,05364

0,04713

0,10968

-0,5200

0,4568

1,0632

490

-0,05814

0,05689

0,08257

-0,7150

0,6996

1,0154

495

-0,06414

0,06948

0,06246

-0,9459

1 ,0247

0,9212

500

-0,07173

0,08536

0,04776

-1,1685

1,3905

0,7780

505

-0,08120

0,10593

0,03688

-1,3182

1,7195

0,5987

510

-0,08901

0,12860

0,02698

-1,3371

1,9318

0,4053

515

-0,09356

0,15262

0,01842

-1,2076

1,9699

0,2377

520

-0,09264

0,17468

0,01221

-0,9830

1,8534

0,1296

525

-0,08473

0,19113

0,00830

-0,7386

1,6662

0,0724

530

-0,07101

0,20317

0,00549

-0,5159

1 ,4761

0,0398

535

-0,05316

0,21083

0,00320

-0,3304

1,3105

0,0199

540

-0,03152

0,21466

0,00146

-0,1707

1,1628

0,0079

545

-0,00613

0,21487

0,00023

-0,0293

1,0282

0,0011

550

0,02279

0,21178

-0,00058

0,0974

0,9051

-0,0025

555

0,05514

0,20588

-0,00105

0,2121

0,7919

-0,0040

560

0,09060

0,19702

-0,00130

0,3164

0,6881

-0,0045

565

0,12840

0,18522

-0,00138

0,4112

0,5932

-0,0044

570

0,16768

0,17087

-0,00135

0,4973

0,5067

-0,0040

575

0,20715

0,15429

-0,00123

0,5751

0,4283

-0,0034

580

0,24526

0,13610

-0,00108

0,6449

0,3579

-0,0028

58

CiE 15:2004

A, nm

7W

9tt)

b{X)

M)

SM

b{X)

585

0,27989

0,11686

-0,00093

0,7071

0,2952

-0,0023

590

0,30928

0,09754

-0,00079

0,7617

0,2402

-0,0019

595

0,33184

0,07909

-0,00063

0,8087

0,1928

-0,0015

600

0,34429

0,06246

-0,00049

0,8475

0,1537

-0,0012

605

0,34756

0,04776

-0,00038

0,8800

0,1209

-0,0009

610

0,33971

0,03557

-0,00030

0,9059

0,0949

-0,0008

615

0,32265

0,02583

-0,00022

0,9265

0,0741

-0,0006

620

0,29708

0,01828

-0,00015

0,9425

0,0580

-0,0005

625

0,26348

0,01253

-0,00011

0,9550

0,0454

-0,0004

630

0,22677

0,00833

-0,00008

0,9649

0,0354

-0,0003

635

0,19233

0,00537

-0,00005

0,9730

0,0272

-0,0002

640

0,15968

0,00334

-0,00003

0,9797

0,0205

-0,0002

645

0,12905

0,00199

-0,00002

0,9850

0,0152

-0,0002

650

0,10167

0,00116

-0,00001

0,9888

0,0113

-0,0001

655

0,07857

0,00066

-0,00001

0,9918

0,0083

-0,0001

660

0,05932

0,00037

0,00000

0,9940

0,0061

-0,0001

665

0,04366

0,00021

0,00000

0,9954

0,0047

-0,0001

670

0,03149

0,00011

0,00000

0,9966

0,0035

-0,0001

675

0,02294

0,00006

0,00000

0,9975

0,0025

0,0000

680

0,01687

0,00003

0,00000

0,9984

0,0016

0,0000

685

0,01187

0,00001

0,00000

0,9991

0,0009

0,0000

690

0,00819

0,00000

0,00000

0,9996

0,0004

0,0000

695

0,00572

0,00000

0,00000

0,9999

0,0001

0,0000

700

0,00410

0,00000

0,00000

1,0000

0,0000

0,0000

705

0,00291

0,00000

0,00000

1,0000

0,0000

0,0000

710

0,00210

0,00000

0,00000

1,0000

0,0000

0,0000

715

0,00148

0,00000

0,00000

1,0000

0,0000

0,0000

720

0,00105

0,00000

0,00000

1,0000

0,0000

0,0000

725

0,00074

0,00000

0,00000

1,0000

0,0000

0,0000

730

0,00052

0,00000

0,00000

1,0000

0,0000

0,0000

735

0,00036

0,00000

0,00000

1,0000

0,0000

0,0000

740

0,00025

0,00000

0,00000

1,0000

0,0000

0,0000

745

0,00017

0,00000

0,00000

1,0000

0,0000

0,0000

750

0,00012

0,00000

0,00000

1,0000

0,0000

0,0000

755

0,00008

0,00000

0,00000

1,0000

0,0000

0,0000

760

0,00006

0,00000

0,00000

1,0000

0,0000

0,0000

765

0,00004

0,00000

0,00000

1,0000

0,0000

0,0000

770

0,00003

0,00000

0,00000

1,0000

0,0000

0,0000

775

0,00001

0,00000

0,00000

1,0000

0,0000

0,0000

780

0,00000

0,00000

0,00000

1,0000

0,0000

0,0000

59

CIE 15:2004

Table B.2. CIE 1964 standard colorimetric observer. Colour-matching functions r 10 (v),
9w(v), b 10 (v) and corresponding chromaticity coordinates r 10 (v), gio(v), bi (v)
for wavenumbers v- 27 750 to 12 250 cm" 1 at 250 cm" 1 intervals.

v, cm" 1

^ (y)

ShoM

bioM

fio(v)

0io(v)

b :o (y)

27750

0,000000079100

-0,000000021447

0,000000307299

0,21674

-0,05877

0,84203

27500

0,00000029891

-0,00000008125

0,00000116475

0,21622

-0,05877

0,84255

27250

0,00000108348

-0,00000029533

0,00000423733

0,21560

-0,05877

0,84317

27000

0,0000037522

-0,0000010271

0,0000147506

0,21471

-0,05877

0,84406

26750

0,0000123776

-0,0000034057

0,0000489822

0,21358

-0,05877

0,84519

26500

0,000038728

-0,000010728

0,000154553

0,21215

-0,05877

0,84662

26250

0,000114541

-0,000032004

0,000462055

0,21032

-0,05877

0,84844

26000

0,00031905

-0,00009006

0,00130350

0,20819

-0,05877

0,85058

25750

0,00083216

-0,00023807

0,00345702

0,20542

-0,05877

0,85335

25500

0,00201685

-0,00058813

0,00857776

0,20155

-0,05877

0,85722

25250

0,0045233

-0,0013519

0,0198315

0, 1 9664

-0,05877

0,86213

25000

0,0093283

-0,0028770

0,0425057

0,19054

-0,05877

0,86823

24750

0,0176116

-0,0056200

0,0840402

0,18339

-0,05852

0,87513

24500

0,030120

-0,010015

0,152451

0,17455

-0,05804

0,88349

24250

0,045571

-0,016044

0,251453

0,16219

-0,05710

0,89491

24000

0,060154

-0,022951

0,374271

0,14619

-0,05578

0,90959

23750

0,071261

-0,029362

0,514950

0,12797

-0,05273

0,92476

23500

0,074212

-0,032793

0,648306

0,10760

-0,04755

0,93995

23250

0,068535

-0,032357

0,770262

0,08498

-0,04012

0,95514

23000

0,055848

-0,027996

0,883628

0,06127

-0,03071

0,96944

22750

0,033049

-0,017332

0,965742

0,03367

-0,01766

0,98399

22500

0,000000

0,000000

1,000000

0,00000

0,00000

1 ,00000

22250

-0,041570

0,024936

0,987224

-0,04283

0,02569

1,01714

22000

-0,088073

0,057100

0,942474

-0,09662

0,06264

1 ,03398

21750

-0,143959

0,099886

0,863537

-0,17567

0,12189

1,05378

21500

-0,207995

0,150955

0,762081

-0,29501

0,21411

1,08090

21250

-0,285499

0,218942

0,630116

-0,50660

0,38850

1,11810

21000

-0,346240

0,287846

0,469818

-0,84156

0,69963

1,14193

20750

-0,388289

0,357723

0,333077

-1,28355

1,18251

1,10104

20500

-0,426587

0,435138

0,227060

-1,81056

1,84685

0,96371

20250

-0,435789

0,513218

0,151027

-1,90754

2,24646

0,66108

20000

-0,438549

0,614637

0,095840

-1,61274

2,26029

0,35245

19750

-0,404927

0,720251

0,057654

-1,08566

1,93108

0,15458

19500

-0,333995

0,830003

0,029877

-0,63511

1,57830

0,05681

19250

-0,201889

0,933227

0,012874

-0,27128

1,25398

0,01730

19000

0,000000

1,000000

0,000000

0,00000

1,00000

0,00000

18750

0,255754

1,042957

-0,008854

0,19828

0,80858

-0,00686

18500

0,556022

1,061343

-0,014341

0,34686

0,66209

-0,00895

18250

0,904637

1,031339

-0,017422

0,47152

0,53756

-0,00908

18000

1,314803

0,976838

-0,018644

0,57844

0,42976

-0,00820

17750

1,770322

0,887915

-0,017338

0,67035

0,33622

-0,00657

17500

2,236809

0,758780

-0,014812

0,75041

0,25456

-0,00497

17250

2,641981

0,603012

-0,011771

0,81714

0,18650

-0,00364

17000

3,002291

0,452300

-0,008829

0,87130

0,13126

-0,00256

60

CiE 15:2004

v, cm" 1

'io(v)

flhoM

M")

Tio(K)

0io(v)

Jbio(v)

16750

3,159249

0,306869

-0,005990

0,91304

0,08869

-0,00173

16500

3,064234

0.184057

-0,003593

0,94438

0,05673

-0,00111

16250

2,717232

0,094471

-0,001844

0,96704

0,03362

-0,00066

16000

2,191156

0,041693

-0,000815

0,98169

0,01868

-0,00037

15750

1,566864

0,013407

-0,000262

0,99168

0,00849

-0,00017

15500

1 .000000

0,000000

0,000000

1,00000

0,00000

0,00000

15250

0,575756

-0,002747

0,000054

1,00470

-0,00479

0,00009

15000

0,296964

-0,002029

0,000040

1,00674

-0,00688

0,00014

14750

0,138738

-0,001116

0,000022

1,00795

-0,00811

0,00016

14500

0,0602209

-0,0005130

0,0000100

1,00842

-0,00859

0,00017

14250

0,0247724

-0,0002152

0,0000042

1,00859

-0,00876

0,00017

14000

0,00976319

-0,00008277

0,00000162

1,00838

-0,00855

0,00017

13750

; 00375328

0,00003012

0,00000059

1,00793

-0,00809

0,00016

13500

0,00141908

-0,00001051

0,00000021

1,00731

-0,00746

0,00015

13250

0,000533169

-0,000003543

0,000000069

1,00656

-0,00669

0,00013

13000

0,000199730

-0,000001144

0,000000022

1,00565

-0,00576

0,00011

12750

0,0000743522

-0,0000003472

0,0000000068

1,00460

-0,00469

0,00009

12500

0,0000276506

-0,0000000961

0,0000000019

1,00342

-0,00349

0,00007

12250

0,0000102123

-0,0000000220

0,0000000004

1,00212

-0,00216

0,00004

Reference

CiE, 1959. Proc. of the 14th Session of CIE, Brussels, Vol. A, 91-109, 1959.

CIE. 1986. CIE S002-1986. CIE standard coiorimetric observers, 1986. (Published also as
CIE/ISO 10527:1991).

CIE, 1990. CIE 86-1990. CIE 1988 2° spectral luminous efficiency function for photopic vision,
1990.

MORREN L, 2000. Private communication, calculations done for the CIE TC 1-48.

SCHANDA, J., 1998. Current CIE work to achieve physiologically correct colour metrics, in
Color Vision, Perspectives from different disciplines, eds.: Backhaus, W.G.K., Kliegl, R.,
Werner, J.S. Walter de Gruyter, Berlin- New York, 1998.

61

C1E 15:2004

APPENDIX C. ALTERNATIVE METHOD TO DEFINE DAYLIGHT ILLUMINANTS -
METHOD OF CALCULATION, CORRECTED TABLES AND EQUATIONS (FOR
INFORMATION AND EVALUATION)

If one tries to apply the calculation procedure for other illuminants D, which is described in
Section 3.1 to D65, one has to follow a rounding process for computing the coefficients M^
and M 2 and then a peculiar practice for rounding the final results. These unusual procedures
explain the slight deviations sometimes observed in comparison with the official table for
standard illuminant D65. These changes are negligible for colorimetric calculations, but are
annoying if tables are compared, see (Kranicz and Schanda, 2000).

Daylight illuminant spectral power distribution tables are based on the work of Judd
and co-workers (Judd et aL, 1964), who proposed the calculation method of daylight
illuminants based on the S , S 1f S 2 component functions. Judd and co-workers published the
So, Si, S 2 functions at 10 nm increments: from these the table accepted by the CIE and
reproduced in Table T.2 was calculated using linear interpolation. (Also Table 1 of the CIE
standard (CIE, 1998) was calculated using linear interpolation.)

Using the equations in Section 3.1 without following carefully the details of use may
lead to slightly different results if the original 10 nm tables, or the 5 nm tables as reproduced
in Section 11. Tables, or the 1 nm tables of the standard are used. To overcome this problem
- and to harmonise colorimetric practice - an alternative method is recommended for
evaluation. Since the interpolation of all other colorimetric functions from their original 10 nm
values has been done by non-linear interpolation, these new tables have been derived by a
Lagrange interpolation method**. The table containing the Lagrange interpolated S 0L a g) S 1Lag
and S 2L ag values of the S 0l S 1f S 2 functions at 1 nm increments is included on the
accompanying CD-ROM. The original Judd and co-workers' 10 nm data were used as input
data. Table C 1 shows the 5 nm sampled set of values.

The starting point for Daylight Illuminant calculation is the set of Equ.'s 3.2, 3.3 and
3.4 of the main publication.

First one has to calculate the x D chromaticity coordinate of the daylight phase
required using Equ. 3.3 for daylight illuminant correlated colour temperatures from
approximately 4000 K to 7000 K, or Equ. 3.4 for daylight illuminant correlated colour
temperatures from larger than 7000 K to approximately 25 000 K.

Then y D is calculated using Equ. 3.2.

These Equ.'s are regarded as defining the daylight chromaticity.

The next step is to calculate the Daylight Illuminant relative spectral power distribution
using these x D , y D values and Equ. 3.5: XXI

S(A) = So(Z) + M,SM) + M 2 S 2 (A) (3.5)

The official CIE method uses the S (A), Si (A), S 2 (X) functions as defined in Table T.2.
These component spectra were originally determined at the full 10 nm increments, and later
linearly interpolated to every 5 nm.

To calculate S(A) one has to know the M u M 2 factors. The original Judd publication
defines these as functions of x D , y D as reproduced in Equ. 3.6: XXI

_ -1,351 5 -1,7703x D + 5,91 14y D
1 ~ 0,0241 + 0,2562x D - 0,7341y D (3 6)

.. 0,030 - 31,4424 x D +30,071 7y D

2

0,0241 + f 2562x D - 0,734 1y D

xx To be able to determine S , S u S 2 values at any desired wavelength, the accompanying
CD-ROM contains a Lagrange interpolation program.

XXI

Equ.'s 3.5 and 3.6 are taken from Section 3 of the present document.

62

CI E 15:2004

The constants in these Equ.'s depend, however, on the sampling of the S functions,
see (Kranicz and Schanda, 2000). The main publication overcomes this difficulty by stating
that calculations have to be done at 10 nm increments with subsequent linear interpolation.

The M 1( M 2 functions can be written in a general form:

M _ gn*D+ft n yD+''n

jx D + ky D + /
where n = 1 for Equ. M-, and n = 2 for Equ. M 2 .

g, h, i, I k and / are obtained as the tristimulus values of the S (A), $i(/l), S 2 (A)
functions, and recommended values are listed in Table C 2. Thus e.g.

gi =10QO B ° D2 " B2Do

D 2

where e.g.

B = £s U)yU)AA and B 2 = Js 2 U) y(l)AA

Anin

and the D symbols refer to the sum of the three tristimulus values of the form as shown by the
B equations for the /tristimulus values of the S , Si and S 2 functions.

The tristimulus values will depend on the method of summation, and thus also the g,
h, i, I k and / coefficients will depend on them. This ultimately will have an influence on the x s ,
y s chromaticity coordinates of the daylight phases calculated from the S(Z) spectral power
distribution according to Equ. 3.5. If these x s , y s values deviate from the x D , y D values used as
the input values in the calculation, a user may feel unsure as to whether he or she has
followed the procedure correctly. To avoid such confusion, values of g n , h n , i n , j, k and / have
to be calculated for the summation used for calculating S(A). Table C.2 shows the
recommended values for the CIE 1931 and CIE 1964 standard observers using the 1 nm
standard tables and the Lagrange interpolated S 0Lag , S 1Lag , S 2 L ag tables, both for 1 nm and 5
nm abridged and truncated colour matching tables. Using these g^ ... i coefficients the x Si ys
values agree with the x D , y D values to five decimal places.

63

CiE 15:2004

Table C.1. S 0L ag, S 1Lag and S 2L ag 5 nm sampled spectra.

X, nm

SoLag

SiLag

S2Lsg

300

0,04000

0,02000

0,00000

305

-0,15625

-0,15000

1,15625

310

6,00000

4,50000

2,00000

315

16,56625

12,50500

2,84375

320

29,60000

22,40000

4,00000

325

43,80000

33,40625

6,41875

330

55,30000

42,00000

8,50000

335

57,62500

42,46250

8,50000

340

57,30000

40,60000

7,80000

345

59,69375

41,23750

7,29375

350

61,80000

41,60000

6,70000

355

61,47500

39,58750

5,88125

360

61,50000

38,00000

5,30000

365

65,46875

40,21875

5,80625

370

68,80000

42,40000

6,10000

375

66,40625

40,94375

4,71250

380

63,40000

38,50000

3,00000

385

62,45000

35,98125

2,05000

390

65,80000

35,00000

1,20000

395

79,82500

38,80000

-0,10000

400

94,80000

43,40000

-1,10000

405

101,54375

45,52500

-0,93125

410

104,80000

46,30000

-0,50000

415

106,54375

45,70625

-0,53125

420

105,90000

43,90000

-0,70000

425

100,35000

40,37500

-0,87500

430

96,80000

37,10000

-1,20000

435

104,05000

36,52500

-1,91250

440

113,90000

36,70000

-2,60000

445

120,82500

36,48125

-2,84375

450

125,60000

35,90000

-2,90000

455

126,54375

34,49375

-2,88125

460

125,50000

32,60000

-2,80000

465

123,39375

30,26875

-2,69375

470

121,30000

27,90000

-2,60000

475

121,52500

26,06875

-2,63750

480

121,30000

24,30000

-2,60000

485

117,42500

22,21875

-2,21875

X, nm

SoLag

$1Lag

S 2 |_sg

490

113,50000

20,10000

-1,80000

495

112,95625

18,07500

-1,61250

500

113,10000

16,20000

-1,50000

505

112,19375

14,74375

-1,38750

510

110,80000

13,20000

-1,30000

515

108,36250

10,86875

-1,25000

520

106,50000

8,60000

-1,20000

525

107,60000

7,18125

-1,12500

530

108,80000

6,10000

-1,00000

535

107,25000

5,13750

-0,75000

540

105,30000

4,20000

-0,50000

545

104,90625

3,05000

-0,38750

550

104,40000

1,90000

-0,30000

555

102,39375

0,90625

-0,15000

560

100,00000

0,00000

0,00000

565

97,78125

-0,80000

0,10000

570

96,00000

-1,60000

0,20000

575

95,67500

-2,65000

0,26250

580

95,10000

-3,50000

0,50000

585

91,95625

-3,47500

1,25000

590

89,10000

-3,50000

2,10000

595

89,43750

-4,56250

2,69375

600

90,50000

-5,80000

3,20000

605

90,60625

-6,55625

3,68125

610

90,30000

-7,20000

4,10000

615

89,61250

-7,93125

4,43125

620

88,40000

-8,60000

4,70000

625

86,01250

-9,05000

4,83750

630

84,00000

-9,50000

5,10000

635

84,47500

-10,26875

5,88750

640

85,10000

-10,90000

6,70000

645

83,52500

-10,80625

7,01875

650

81,90000

-10,70000

7,30000

655

81,90625

-11,21250

7,91250

660

82,60000

-12,00000

8,60000

665

84,01875

-13,10625

9,25625

670

84,90000

-14,00000

9,80000

675

83,83125

-14,02500

10,19375

64

CIE 15:2004

X, nm

^OLag

Snag

$2Lsg

680

81,30000

-13,60000

10,20000

685

76,22500

-12,69375

9,19375

690

71,90000

-12,00000

8,30000

695

72,38125

-12,57500

8,90000

700

74,30000

-13,30000

9,60000

705

76,31875

-13,32500

9,22500

710

76,40000

-12,90000

8,50000

715

69,45625

-11,66250

7,64375

720

63,30000

-10,60000

7,00000

725

66,35000

-10,91875

7,18125

730

71,70000

-11,60000

7,60000

735

75,61250

-12,08750

7,91875

740

77,00000

-12,20000

8,00000

745

72,52500

-11,38750

7,46875

750

65,20000

-10,20000

6,70000

755

54,40625

-8,66250

5,73125

X, nm

£>OLag

S"ILag

^2Lsg

760

47,70000

-7,80000

5,20000

765

57,28125

-9,40000

6,24375

770

68,60000

-11,20000

7,40000

775

68,04375

-11,00000

7,22500

780

65,00000

-10,40000

6,80000

785

65,58750

-10,50625

6,90000

790

66,00000

-10,60000

7,00000

795

64,04375

-10,25000

6,76875

800

61,00000

-9,70000

6,40000

805

56,48750

-8,88125

5,87500

810

53,30000

-8,30000

5,50000

815

55,43125

-8,68125

5,71875

820

58,90000

-9,30000

6,10000

825

61,71875

-9,79375

6,43125

830

61,90000

-9,80000

6,50000

Table C.2. g 1 to / coefficients for CiE 1931 and 1964 standard observers and 1 nm standard
tables using the Lagrange interpolated S , Si and S 2 functions both for 1 nm and 5 nm
sampling.

Coeff.s

CIE 1931 St.
Obs.

1 nm sampling

CIE 1964 St.
Obs.

1 nm sampling

CIE 1931 St.
Obs.

5 nm sampling

CIE 1964 St.
Obs.

5 nm sampling

Qi

-1 ,77864

-1 ,57049

-1,77861

-1,57049

Ai

5,90745

5,56450

5,90757

5,56460

/i

-1,34666

-1,31211

-1,34674

-1,31215

92

-31,44505

-30,15166

-31,44464

-30,15139

h 2

30,06408

31,07906

30,06400

31,07931

h

0,03656

-0,73912

0,03638

-0,73928

J

0,25540

0,21249

0,25539

0,21250

k

-0,73218

-0,71591

-0,73217

-0,71592

1

0,02387

0,04663

0,02387

0,04663

References

CIE, 1998. CIES005/E:1998. CIE standard iiluminants for colorimetry. (Published also as ISO
10526:1999(E)/CIE S 005-1998), 1998.

JUDD, D.B., MACADAM, D.L. and WYSZECKI, G., 1964. with the collaboration of BUDDE,
H.W., CONDIT, H.R., HENDERSON, ST, and SIMONDS, J.L Spectral distribution of typical
daylight as a function of correlated color temperature. J. Opt. Soc. Am. 54, 1031-1040, 1964.

KRANICZ, B. and SCHANDA, J., 2000. Re-evaluation of daylight spectral distributions. Color
Res. AppL, 25 (4), 250-259, 2000.

65

CiE 15:2004

APPENDIX D. REVERSE TRANSFORMATION FROM VALUES L*, a*, b* TO
TRISTIMULUS VALUES X, Y, Z

In Information Technology (IT) transformations are necessary from the tristimulus values X, Y,
Z to the values L*,a*,b* and in the reverse [R] direction, Therefore it was decided at the TC
meetings in Veszprem in August 2002 to include a proposed reverse transformation into CIE-
Publication 15 "Colorimetry". The first transformations are given in the main part of the
document (see Section 8.2.1) and the reverse transformations are in this Appendix D.

Reverse transformation:

Calculate from the values L*, a*, b*

/(Y/Yn)=(L*+16)/116 (D.1)

f(X/Xn)=a*/ 500 +/( Y/Y n ) (D.2)

f(Z/ZnK(Y/Y n )-jb*/200 (D.3)

Calculate then the tristimulus values X, Y, Z from:

X^Xn[/(X/Xn)] 3 if f(X/Xn) > 24/1 16 (D.4)

X=Xn[fl[X/Xn) - 16/1 16]x(108/841) if f[X/Xn) < 24/1 16 (D.5)

Y=Yn[/(Y/Yn)] 3 if f[Y!Yn) > 24/1 16 or L*> 8 (D.6)

Y=Yn[/(Y/Yn)-16/116]x(108/841) if /(Y/Yn) < 24/116 or L*< 8 (D.7)

Z=Zn[/(Z/Zn)] 3 if /(Z/Zn) > 24/116 (D.8)

Z=Zn[/{Z/Zn) - 16/11 6]x( 108/841) if /(Z/Zn) < 24/116 (D.9)

Note: Integer ratios, e. g. 16/116, 841/108, 108/841, are used for both transformations to
avoid rounding errors. The break point between the non-linear and the linear part of
the values L* is at L* =8 as proposed by Pauli (1976).

Reference

PAUL!, H., 1976. Proposed extension of the CIE recommendation on "Uniform color spaces,
color difference equations, and metric color terms". J. Opt. Soc. Am., 66, 866-867, 1976.

66

CIE 15:2004

APPENDIX E. INFORMATION ON THE USE OF PLANCK'S EQUATION FOR STANDARD
AIR

According to the Planck's law, the spectra! radiance of a blackbody at thermodynamic
temperature 7"[K] in a medium having index of refraction n is given by

^ r >=°^

exp i^h

(E.1)

where c^ = 2%hc 2 , c 2 - hclk, h is Planck's constant, c is the speed of light in vacuum, k is the
Boitzmann constant, and k is the wavelength in the medium. Since T is measured on the
International Temperature Scale, the value of c 2 used in colorimetry should follow that
adopted in the current international Temperature Scale (ITS-90) (Preston-Thomas, 1990;
Mielenz et al., 1991), namely c 2 - 1,4388 x 10" 2 m K. The official value of c^ is provided by the
Committee on Data for Science and Technology (CODATA), and is d = 3,741 771 x 10" 16
W m 2 (Mohr and Taylor, 2000). The value of c u however, is not relevant in colorimetry where
only the relative spectral distribution of Planck's radiation is used.

The value of n of air depends on the partial pressure of each constituent of the air
and is also wavelength dependent, but for standard air (dry air al 15°C and 101 325 Pa,
containing 0,03 percent by volume of carbon dioxide), it is approximately 1,00028 throughout
the visible region. This value has been used in photometry and radiometry for a number of
years (Blevin, 1972), and is confirmed from the latest physical data showing n more precisely
as a function of wavelength (Cohn et al., 2003).

Using Equ. E.1 with n - 1,00028, CIE standard illuminant A can be calculated, with
negligible differences from the published values (1 count or less in the 6th significant digit), by

i-*Ak, T)

S A (k) = exV — (E.2)

L. iA (660nm, T)

where c 2 = 1,4388 x10" 2 m-K (ITS-90) and 7" = 2854,742 K. This temperature T is the value
assigned to CIE standard illuminant A in the Planck's equation for standard air. This implies
that correlated colour temperature of CIE standard illuminant A should be -2855 K, a change
of -1 K from the previous value (2856 K). However, TC 1-48 did not come to a consensus at
this time to revise the definition of correlated colour temperature using n = 1,000 28, because
the form of Pianck's equation in vacuum (n is equal to exactly 1) has been used historically
and it was concerned that such a revision would cause a small discontinuity from the values
obtained in the past (though the difference is practically insignificant and matters only in
rigorous calculations). It was also concerned that the revision still would not describe Planck's
radiation in air perfectly; the value of n is slightly wavelength dependent, which would bring
the CIE standard illuminant A deviating very slightly off from a perfect Planckian radiator
(though the deviation would be less than 0,005% - calculated using data in Cohn et al.,
2003.

Therefore, in the current recommendation in CIE 15:2004, colour temperature and
correlated colour temperature are calculated using Equ. E.1 with n-1 (exactly 1), thus no
change from the previous practice. This recommendation may be subject to change in the future.

References

BLEVIN, W.R., 1972. Corrections in Optical Pyrometry and Photometry for the Refractive
Index of Air. Metrologia, 8, 140-147, 1972.

COHN, E.R, LIDE, D.R. and TRIGG, G.L., Editors, 2003. AIP Physics Desk Reference. Third
Edition. Springer-Veriag, 2003.

MIELENZ, K.D., SAUNDERS, R.D., PARR, A.C. and HSIA, J.J., 1991. The New International
Temperature Scale of 1990 and its Effect on Radiometric, Photometric, and Colorimetric
Measurements and Standards, in CIE 91-1991. Proc. of the 22 nd Session of the CIE, D2, 65-
68,1991

MOHR, P.J. and TAYLOR, B.N., 2000. CODATA recommended values of the fundamental
physical constants: 1998. Reviews of Modern Physics, 72/2, 351-495, 2000.

67

CiE 15:2004

PRESTON-THOMAS, H., 1990. The International Temperature Scale of 1990, Metrologia 27,
3-10, 1990.

EXPLANATORY COMMENTS

1 CIE Division 1 (at its meeting in Rochester in 2001) and CIE Division 2 (at its meeting
in Gaithersburg in 2001) confirmed that wavelengths measured in standard air (dry air
at 15°C and 101 325 Pa, containing 0,03 percent by volume of carbon dioxide) should
be used in ail CIE publications.

2 This recommendation deviates from earlier recommendations regarding CIE sources
A, B, C (CIE, 1931; CIE, 1951). A distinction is made between illuminant and source.
The term source refers to a physical emitter of light, such as a lamp or the sun and
sky. The term illuminant refers to a specific spectral power distribution, not
necessarily provided directly by a source, and not necessarily realizable as a source.
The present recommendation first defines illuminants by relative spectral power
distributions and then sources. The definition of the sources is considered secondary,
as it is conceivable that new developments in lamps and filters will bring about
improved sources that represent the illuminants more accurately and are more
suitable for laboratory use. At present, no recommendation has been made for a
source representing standard illuminant D65. The original recommendations
regarding standard illuminant D65 (originally called D 65 ) and other illuminants D
representing daylight of different correlated colour temperatures are given in CIE
Proceedings (CIE, 1963; CIE, 1967).

In 1968 the Comite International des Poids et Mesures modified the "International
Practical Temperature Scale, 1948 (amended 1960)" and the value of the radiation
constant c 2 was set equal to 1,4388-10 i2 m-K. This modification has affected the
colour temperature or correlated colour temperature of the CIE illuminants and
sources.

3 Equation 3.1 is equivalent to and can be derived from the expression

S(X) = 100 M e ^(X,T) I M ej /( 560, 7), (EN.1)

where

Me^UT) = Ci ^ [exp(c 2 I XT) - if, (EN.2)

X is the wavelength (in nanometres), and the ratio c 2 /7~is given by

c 2 /r= 1,435 x 10 7 /2 848 nm (EN.3)

Since the numerical value of c^ cancels out of Equ. E.1, this definition of CIE standard
illuminant A involves no assumptions about the numerical values of d, c 2 , and T other
than the ratio defined in Equ. E.3. (See CIE 1998c).

CIE standard illuminant A was originally defined in 1931 as the relative spectral
power distribution of a Planckian radiator of temperature

7ciei9 3 i=2 848K, (EN.4)

the value of the second radiation constant c 2 then being taken as

c 2 , cie 1931 = 1 ,435 x 10~ 2 m-K. (EN. 5)

The form of the definition as now printed was carefully chosen to ensure that CIE
standard illuminant A was defined as a relative spectral power distribution and not as
a function of temperature; as explained above, the definition of the relative spectral
power distribution has not changed since 1931 and Equ. 3.1 simply expresses it in a
general form.

What has changed is the temperature assigned to this distribution. The value of c 2
given in Equ. E.5 and used by the CIE in 1931 is different from the respective values,
c 2 ,its-27 = 14 350 urn-K, c 2J p T s-48 = 14 380 urrvK, and c 2 j PT s-68 = c 2i rrs~9o = 14 388 um-K,
that were assigned to this constant in the International Temperature Scales of 1927,

68

CI E 15:2004

1948, 1968 and 1990, respectively. Although this has had no effect on the relative
spectral power distribution of CIE standard iiiuminant A, the correlated colour
temperatures of sources recommended for laboratory realizations have been
different, over the years, depending on the values of c 2 used. As may be seen from
Equ. E.3, the colour temperatures associated with CIE standard iiiuminant A on the
various international temperature scales referred to above were 7" 2 7 - 2 848 K, T 48 -
2 854 K, and 7" 68 = T 90 = 2 856 K, respectively.

Another change over the years has been the explicit decision that the wavelengths in
Equ.'s 3.1, E.1 and E.2 should be taken as being in standard air despite the fact that
the equations are derived from the form of Planck's equation in vacuum. The Planck's
equation requires a refractive index term if the wavelengths refer to a medium other
than vacuum. Iiiuminant A was originally defined in 1931 as the relative spectral
distribution of a Planckian radiator but, historically, wavelengths in standard air have
always been used in photometry and colorimetry. Despite this, CIE/ISO 10526:1991
and its revision, ISO 10526:1999(E)/CIE S 005-1998, stated that the term A denoted a
wavelength in vacuum. This was inconsistent with previous CIE publications, but the
situation was not addressed until recently. CIE Division 1 and Division 2 agreed in
2001 that all wavelengths used in CIE Publications should be in standard air
(explanatory comment 1). The current document follows this decision. ISO
10526:1999/C!E S 005-1998 is also to be revised to reflect this change (CIE S 014-2
to be published). The use of standard air wavelengths means that the colour
temperature of iiiuminant A is very slightly different from the values of T used in the
above equations but the difference is insignificant for ail practical purposes. See
Appendix E for further information on the use of Planck's equation for standard air.

It is important to note that the numerical values defined for CIE standard iiiuminant A
have never changed. The only issues have been the change of temperature scale
and the use of standard air. The 1 nm tables given in CIE standard S005 and
reproduced on the CD-ROM accompanying this report are consistent with Equ. 3.1. In
cases where calculation at 5 nm intervals is found to produce no significant error, the
data in Table T.1 can be used.

The rounded values of S(A) for CIE standard iiiuminant A given in Table T.1 show, in
several instances, small and insignificant discrepancies of one unit in the last decimal
from corresponding values commonly used in various publications. The values given
in Table T.1 are the correctly rounded values and agree with those of the standard.

The correlated colour temperatures are affected by the numerical value of the
radiation constant c 2 . In accordance with the International Practical Temperature
Scale, 1948, amended 1960 which was in use at the time when the procedure for
calculating daylight illuminants was adopted by the CIE, the value of c 2 was equal to
1,438 x 10" m-K. With this value, the correlated colour temperature of iiiuminant
D65 is approximately equal to 6500 K. The change of c 2 to the value of 1 ,438 8 x 10" 2
m-K (International Practical Temperature Scale, 1968) increases the correlated colour
temperatures of iiiuminant D65 by the factor 1,4388/1,4380. Thus the correlated
colour temperature increases by approximately 4 K.

The method required to calculate the values for the relative spectral power
distributions of illuminants D50, D55, D65, and D75, in Table T.1 is as follows

1. Multiply the nominal correlated colour temperature (5000 K, 5500 K, 6500 K or
7500 K) by 1,4388/1,4380.

2. Calculate x D and y D using the equations given in the text.

3. Calculate M^ and M 2 using the equations given in the text.

4. Round M, and M 2 to three decimal places.

5. Calculate S(A) every 10 nm by S(Z) = S D (A) + M r S^(A) + M?S 2 (X) using values of
S (A), SiU) and S 2 (Z) from Table T.2.

6. Interpolate the 10 nm values of S(A) linearly to obtain values a\ intermediate
wavelengths.

69

CIE 15:2004

This method should also be followed to calculate the relative spectral power
distribution of illuminants at other nominal correlated colour temperatures.

6 This recommendation supersedes the original (CIE, 1931) and is in accordance with
a later agreement (CIE, 1959).

7 This recommendation has been changed from the original (CIE, 1931) method
several times, see joint meeting of E-1.3.1, E-1.3.2 and E-1.2 on June 28, 1967 in
Washington (CIE, 1967). The present version is the result of a major updating, as
colorimetric practice has shown that more precise definitions of measuring geometry
are needed. Regarding practical measurements see aiso (CIE, 1998d).

8 Where single-beam integrating spheres are used, a correction for the reduction of
sphere efficiency caused by sample absorption is necessary. Without such a
correction, the instrument will give a non-linear output. The corrected reflectance is
given by:

o = R n) 1-p w (A)-(1-y y )

S ^'l-^.tl-S^-fs.^)-^))'

where R(X) is the uncorrected reflectance of the sample referred to the perfect
reflecting diffuser, p^(X) is the diffuse/diffuse spectral reflectance of the sphere wall, /j-
is the fractional area of the /th port, f s is the fractional area of the sample port, and
p T (X) is the reflectance of the reference standard. The above equation assumes idea!
integrating characteristics for the sphere and that the other ports have zero effective
reflectance.

9 These recommendations are based on the originals (CIE, 1931; CIE, 1959; CIE,
1963).

The recommendations given in this document regarding the CIE 1931 standard
colorimetric observer data deviate from the originals in several ways. The CIE 1931
standard colorimetric observer is now defined by the colour-matching functions x(X),

y{X), z(X) from 360 nm to 830 nm at 1 nm intervals (see Table 1 in CIE, 1986a).
From these data the abridged data reproduced in Table T.4. have been derived by
selecting every fifth value and rounding to six decimal figures.

10 Colour-matching functions x(X), y(X), z(X) are relative tristimulus values of
monochromatic radiators of equal radiant power related to a set of reference stimuli
[X], [Y], [Z].

11 The colour-matching functions x(A), y(A), z{X) given in Table T.4 agree closely
with those defined originally in 1931. Three minor changes have been introduced: at
X =775 nm the new values of x(X) is 0,000 059 instead of 0,0000; at X = 555 nm
y(X) is 1,0000 instead of 1,0002; and at X = 740 nm y(X) is 0,000 249 instead of
0,0003. These changes are considered insignificant in most colorimetric
computations. From these corrected tables the CIE standard colorimetric observer
(CIE, 1986a) was determined.

12 For daylight illuminant D65 2,464 scotopic trolands corresponds to 1 photopic troland
(see Wyszecki & Stiles, 1982, p. 104). Rod saturation in 9° extrafoveai vision occurs
at about 2000-5000 scotopic trolands (see Wyszecki & Stiles, 1982, p. 547). Thus rod
saturation would occur at a photopic light level of between 812-2 029 trolands.
Working from the Table in Le Grand (1968, p. 106) that takes into account variation of
pupil size with light level and the Stiles-Crawford effect, this would correspond to 130-
380 cd/m 2 (kind contribution by J. Pokorny).

13 These recommendations formalise procedures for practical colorimetric calculations.

14 CIE 15:2004 states only the facts on abridgement and truncation. A forthcoming
publication of a tutorial nature will detail the procedures, with examples showing good
practice.

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C!E 15:2004

15 This recommendation is based on the original (CIE, 1955) amended in CIE Bulletin
No. 3, (CIE, 1957). The use of boldface Roman letters as symbols for vector
notations is another alternative which was added in the first edition of this publication.
In the present 3rd edition of the document the recommendation to use "Gothic letters"
has been dropped.

16 These recommendations are based on those given in supplement No. 2 to the 1st
edition of this publication (CIE 1978), the publication on "Industrial colour difference
evaluation" (CIE 1995a) and the publication "Improvement to industrial colour
difference evaluation" (CIE, 2001a), with some amendments agreed at TC 1-48 and
TC 1-59 meetings in Veszprem, 2002 and San Diego, 2003.

17 In June 1967 the CIE coiorimetry committee recommended to the National
Committees of the CIE a detailed working program for pursuing the problem of colour
difference calculations (Wyszecki, 1968). Further guidelines were published in 1978
(Robertson, 1978). The parametric effects in colour difference evaluation were
summarised in 1993 (CIE, 1993), and an advanced colour difference calculation
method was published in 1995 (CIE, 1995a). Recent findings are summarized in
(CIE, 1999a). The currently recommended colour difference formula is described in
(CIE, 2001a).

18 Equations (8.7), (8.9) and (8.11) are based on a suggestion by Pauii (1976),
according to which below L*=8 a linear L*=f(Y) dependence should be followed. In
CIE 15.2 decimal approximations were used. This brought the break point of Y/Y n =

\3 1 Tl 1fi ^

to 0,008856, and the exact value of -x to 7,787. At the Technical

116 J 3 ^ 24 j

Committee TC 1-48 meeting in Veszprem, 2002, the committee agreed that to secure
the continuity at the break between the two parts of the equations f{Aji A in ), where

A^- X, A 2 = V, y4 3 = Z, f-=^-| should be written instead of its approximate value of

1 f i Ifi^ 2 841

0,008 856, and similarly — x should be used instead of 7,787 in Equ.'s

3 1,24 J 108

(8.7), (8.9) and (8.11).

19 This recommendation is essentially the same as the original (CIE, 1948).

20 Previous two publications Special metamerism index: Change in iiluminant
(Supplement No. 1 to 1st edition of CIE 15-1971 (CIE, 1971) and Special metamerism
index: Change in observer (CIE, 1989) have been combined in this version of CIE 15.
CIE 80-1989 is, however, still current, and provides more details on the subject.

21 Table T.6 gives the relative spectral power distributions of 15 FL-illuminants that
represent 15 different types of fluorescent lamps.

The FL1 to FL12 group of lamps were also included in 15.2 (there as F1 to F12). The
further spectra are enumerated by starting with the number 3, reflecting that they
have been first introduced when elaborating version 3 of CIE 15. Each of the relative
spectral power distributions in the standard halophosphate ("St-Halo") group (FL3.1-
3.3) consists of two semi-broadband emissions of antimony and manganese
activations in a calcium halo-phosphate phosphor. The "DeLuxe" group (FL 3.4-3.6)
are more or less enhanced in colour rendering properties as compared to the
"St-Halo" group, usually using multiple phosphors. Relative spectral power
distributions of the "DeLuxe" group are flatter and have a wider range in the visible
spectrum than the "St-Halo" group. Relative spectral power distributions of the
"Three-band" group (FL3.7-3.11) consist mostly of three narrow-band emissions in
the red, green, and blue wavelength regions. In most cases the narrow-band
emissions are caused by ternary compositions of rare-earth phosphors. FL3.12-3.14
represent modern multiband fluorescent lamp spectra. FL3.15 is the spectrum of a
fluorescent lamp developed commercially to simulate D65, taken from JIS 8716 (JIS,
1991).

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CIE 15:2004

22 In many applications high-pressure metal-halide and sodium lamps are gaining in
importance. Spectra, as reproduced in Table T.7, with colorimetric data shown in
Table T.9, are representative spectra of these classes of sources and could be used
for checking colorimetric properties of objects when illuminated with such lamps.

23 This is a new Section in the document based on CIE 51, first published in 1981 for
assessing illuminants D55, D65 and D75 (CIE, 1981), and amended in 1999 with a
technique to assess the quality of D50 illuminants (CIE, 1999b).

24 The daylight simulators having suitable categories, as assessed by the method in this
report, can be used to simulate standard illuminants D50, D55, D65and D75for visual
matching of object-colour samples, and for reproducing the spectral total radiance
factor of samples for instrumental colorimetry and spectrophotometry; the samples
may be non-fluorescent or fluorescent.

The daylight simulators may also be used for the visual appraisal of the colour
rendering properties of other light sources, though the present method of evaluation
for daylight simulators does not directly relate to the evaluation of colour rendering
properties.

25 This recommendation was published for the first time in the edition 15.2-1986 of this
publication.

26 This section has been updated according to the decisions of CIE Division 1 obtained
at its meeting in Rochester, USA, 2001.

72